Article
Design Parameters of V ortex Pumps: A Meta-Analysis
of Experimental Studies
Angela Gerlach 1, ∗ , Paul Uwe Thamsen 1 , Sebastian W ulf f 1 and Christian Brix Jacobsen 2
1 Department of Fluid System Dynamics, T echnische Universitaet Berlin, Strasse des 17.Juni 135,
10623 Berlin, Germany; [email protected] (P .U.T .); [email protected] (S.W .)
2 Mechanical Development, Grundfos Holding A/S, Poul Due Jensen V ej 7, 8850 Bjerringbro, Denmark;
[email protected]
* Correspondence: [email protected] ; T el.: +49-30-314-79707
Academic Editor: Leonardo P . Chamorr o
Received: 14 November 2016; Accepted: 29 December 2016; Published: 5 January 2017
Abstract:
V ortex pumps can impel solid-containing fluids and are ther efor e widely applied, fr om
wastewater transport to the food industry . Despite constant ef forts to impr ove vortex pumps,
however , they have r emained r elatively inef ficient compar ed to conventional centrifugal pumps.
T o find an optimized design of vortex pumps, this paper pr ovides a systematic analysis on
experimental studies that investigated how variations in geometric parameters influence vortex
pump characteristics, in particular the pump head, the pr essur e coef ficient and the ef ficiency for best
point operation. T o this end, an extensive literature sear ch was conducted, and eighteen articles with
53 primary investigations wer e identified and meta-integrated. This showed that it is not yet clarified
how vortex pumps operate. T wo dif fer ent assumptions of the underlying operating principle of
a vortex pump lead to diver ging design principles. Fr om the r esults of this meta-analysis, we deduce
r ecommendations for a mor e ef ficient design of a vortex pump and emphasize further aspects on the
underlying operating principle of a vortex pump.
Keywords:
vo rt ex p um p ; r e ce ss ed i m pe ll er ; en l ar ge d si de cha mbe r; m et a-an aly si s; d es ign pa ram et er s;
op er atin g pri nc ip le; ex per im en tal st udi es
1. Introduction
The semi-open, r ecessed impeller and the enlarged side gap at the fr ont chamber are the
characteristics of vortex pumps that impel fluids with solid and fibr ous material at a minimal risk
of clogging. However , the ef ficiency of vortex pumps has remained r elatively poor compared to
conventional centrifugal pumps. In times of raising ener gy prices and strict ener gy goals that aim
at slowing climate change, designing more ef ficient vortex pumps seems more desirable than ever .
The aim of this paper is to find an improved design of vortex pumps in terms of ef ficiency and flow
characteristics. T o this end, an extensive literature sear ch was conducted. Eighteen articles wer e
identified and meta-integrated. All articles varied geometrical aspects in the impeller and/or the
casing and then r eported the pump characteristics. Fr om these r esults, we deduce recommendations
for a mor e ef ficient design. The literature sear ch revealed that vortex pumps wer e designed according
to two diver ging design principles: the covered design or the open design. Both ar e based on dif fer ent
assumptions of the underlying operating principle of a vortex pump.
This r eview focuses on journal articles and conference articles that wer e publicly available at
the time of the literature sear ch. Eligible articles include single-parameter and/or multi-parameter
experimental setups that measur ed how the geometry of the impeller and/or the geometry of the casing
influenced the vortex pump characteristics (e.g., its head and efficiency). The results of computer -based
simulations wer e excluded, but occasionally r eferr ed to if they contributed to a better compr ehension
Energies 2017 , 10 , 58; doi:10.3390/en10010058 www .mdpi.com/journal/energies

Energies 2017 , 10 , 58 2 of 23
of the material pr esented. From spring 2015 until autumn 2015, we sear ched the databases of Google
Scholar (https://scholar .google.com) for all articles containing the following keywords in the title
or abstract: vortex pump, tur o pump, recessed impeller , volute width, enlarged gap, side chamber
gap, centrifugal pump. Because a large number of Chinese articles wer e found in the initial search, an
additional sear ch was conducted in spring 2015 using the database of the China Academic Journal
Electr onic Publishing House (http://www .cnki.net) and the corr esponding Chinese keywords. All hits
wer e scanned with r espect to their validity and content. The final sample contained 18 articles with
53 primary investigations. All of the eligible articles presented single-parameter experiments that vary
only one configuration at a time while holding all other configurations constant.
Figur e 1 and T able 1 list all consider ed parameters in both the single-parameter and the
multi-parameter experiments. Additionally , T able 1 identifies the articles that provided the empirical
base for assessing these parameters. The geometric design parameters and the operation data of the
Best Ef ficiency Point ( BEP ) wer e extracted fr om all articles. If the values were not explicitly mentioned,
we estimated them fr om the r espective graphs.
Figure 1. Considered parameters of a vortex pump.
T able 1. Assessed parameters in the articles.
Assessed Parameter Prefix Source(s)
Impeller
Impeller width b 2
Rütschi [ 1 ], Guan et al. [ 2 ] ([ 3 ]), W ang [ 4 ]-a,
W ang [ 4 ]-b, Zheng et al. [ 5 ], Sha et al. [ 6 ],
Sha et al. [ 7 ], Sha et al. [ 8 ], Ohba et al. [ 9 ],
Masanori [ 10 ]
Impeller diameter D 2
Rütschi [ 1 ], Guan et al. [ 2 ] ([ 3 ]), W ang [ 4 ]-c,
W ang [ 4 ]-d, Zheng et al. [ 5 ], Sha et al. [ 6 ],
Sha et al. [ 7 ], Sha et al. [ 8 ], Ohba et al. [ 9 ]-a,
Ohba et al. [ 9 ]-b, Lubieniecki [ 11 ]-a,
Lubieniecki [ 11 ]-b, Lubieniecki [ 11 ]-c
Blade number z Rütschi [ 1 ], Guan et al. [ 2 ] ([ 3 ]), Masanori [ 10 ],
Blade outlet angle β 2 Guan et al. [ 2 ] ([ 3 ]), Sha et al. [ 6 ], Sha et al. [ 8 ],
Masanori [ 10 ]
Blade inlet angle β 1 Guan et al. [ 2 ] ([ 3 ])
Blade thickness t Guan et al. [ 2 ] ([ 3 ])
W inglets and front shr oud - Zheng et al. [ 5 ], Jiang et al. [ 12 ] ([ 13 ]),
Gerlach et al. [ 14 ]

Energies 2017 , 10 , 58 3 of 23
T able 1. Cont.
Assessed Parameter Prefix Source(s)
Casing
V olute width b 4
Zheng et al. [
5
] ([
15
]), Sha et al. [
6
],
Sha et al. [ 7 ]
,
Sha et al. [ 8 ], Ohba et al. [ 9 ]
Covering s Rütschi [ 1 ]-a, Rütschi [ 1 ]-b, Sha and Hou [ 16 ]
Suction pipe diameter D s Guan et al. [ 2 ] ([ 3 ]), Zheng et al. [ 5 ],
Sha et al. [ 6 ], Ohba et al. [ 9 ]
Geometry of suction inlet pipe - Rütschi [ 1 ]
Pr essur e pipe diameter D d Zheng et al. [ 5 ]
Geometry of casing - Zheng et al. [ 5 ]
Rotation speed n Li and Feng [ 17 ]-a, Li and Feng [ 17 ]-b,
Sha and Bai [ 18 ] ([ 19 ])
Note: Articles in parenthesis used the same experimental results as the afor ementioned articles did.
Some authors investigated the influence of a parameter on slight dif ferent configurations of a
vortex pump and published it in the same article. For example, the author W ang [
4
] investigated the
influence of impeller width on an impeller with a diameter of 195 mm, but also tested the influence of
impeller width on an impeller with a diameter of 180 mm. T o distinguish between these two primary
investigations of the same article for the same assessed parameter , we used the notation W ang [
4
]-a for
the first primary investigation and W ang [
4
]-b for the second primary investigation (cp. second column
of T able 1 ). Similar , it applies to studies of other authors (e.g., for the impeller diameter as assessed
parameter: W ang [
4
]-c and W ang [
4
]-d ; Ohba et al. [
9
]-a and Ohba et al. [
9
]-b; Lubieniecki [
11
]-a,
Lubieniecki [
11
]-b and Lubieniecki [
11
]-c). Ther efor e, T able A1 of the Appendix summarizes the
geometry data of the 53 primary investigations.
Several studies wer e not integrated into this r eview because of their internal scaling (e.g., [
20
–
22
]),
missing data (e.g., [
15
]), ambiguous repr esentation of the data (e.g., parts of [
2
]), non-experimental
natur e and/or missing validation of the simulations (e.g., [
23
–
29
]). Some primary studies varied more
than one parameter at a time when r eporting the characteristics ([
1
,
2
,
4
,
9
,
11
,
17
] and [
8
] (similar in [
30
])).
However , the primary studies were limited to single-parameter investigations because it is the only
setup that allows isolating how distinct variations af fect the BEP s. Further , deductions can be hardly
derived fr om the multi-parameter investigations due to missing data and missing parameter variations.
2. Design Principles of V ortex Pumps
The literatur e sear ch r evealed that vortex pumps wer e designed accor ding to one of two design
principles: the cover ed design or the open design.
2.1. Cover ed Design
In the cover ed design (Figur e 2 a), the impeller is set back into the casing, and the casing thus
completely covers the radial impeller outlet (as Figure 2 b illustrates). Resear chers who follow this
design concept likely assume that the operating principle of vortex pumps is comparable to a hydraulic
coupling, wher e the impeller induces a vortex in the enlar ged side chamber and ther eby transports the
fluid (e.g., [
11
,
29
]). Given that this operating principle is at work, it seems most beneficial to cover the
impeller to the casing. Doing so allows the forming of str onger vortices in the fr ont chamber . Hence,
the working transmission of the impeller would r elease its for ce to the fluid on the fr ont side, and only
small losses occur at the radial exit of the impeller . The literature sear ch yielded that at least 32 out of
53 articles used the cover ed design, while the exact design was unspecified in 13 articles.

Energies 2017 , 10 , 58 4 of 23
The cover ed design is sometimes associated with pan impellers whose shape is either r ectangular
(Figur e 3 a) or r ound (Figur e 3 b). Both impellers wer e likely designed with the intent to optimize
the vortex formation. The geometric closing of both impellers’ radial outlet cr eates an axial energy
transfer to the side chamber . In this case, the round shape (Figur e 3 b) seems the more suitable form
because the r ound shape guarantees a better guidance of the fluid flow . Overall, it is noteworthy that a
pan impeller is not a necessity for the covered designs, although eight out of the 32 investigations on
cover ed designs used them ([ 9 , 10 ]).
V arious authors developed fluid transport models for the cover ed designs and pan impellers.
For example, Schivley and Dussourd [
20
], Aoki ([
31
,
32
]) and Ohba and colleagues ([
9
,
22
,
33
]) developed
pr edicting methods for the performance and design methods for vortex pump impellers.
( a ) ( b )
Figure 2.
(
a
) V ortex pump accor ding to the covered design; and (
b
) schematic illustration of the
covered design.
( a ) ( b )
Figure 3. Examples of pan impellers. ( a ) Rectangular shape; and ( b ) rounded shape.
2.2. Open Design
An alternative design principle of vortex pumps is the open design. Her e, the casing does not
cover the impeller . Instead, the vortex pump looks similar to a centrifugal pump with a semi-open
impeller and wide fr ont gap (Figur e 4 a,b). The assumed operating principle is that of a conventional
centrifugal pump: fluids are transported thr ough the impeller itself and without the assistance of
a vortex. Due to the wide front gap, however , exchange losses occur . These losses would explain
the r elatively low efficiency and the r elatively low head of vortex pumps compared to conventional
centrifugal pumps (e.g., [
1
]). Given that the working principles of vortex pumps and conventional
pumps ar e similar , it follows that comparable design recommendations apply to vortex pumps as they
do to conventional centrifugal pumps. For example, an impeller overlapping with the casing would
disrupt the outflow fr om the impeller and, hence, increase losses.

Energies 2017 , 10 , 58 5 of 23
In the open design, the impeller frequently r esembles a semi-open impeller , similar to that of
a conventional centrifugal pump. The blades ar e curved or straight and, in both cases, pulled up to
the hub (Figur e 5 a,b). This design can be modified when winglets are added to the fr ont edges of the
blades. Figure 6 a is an example of an impeller with winglets. The maximal execution on winglets
r esults in a fr ont shr oud (Figur e 6 b).
( a ) ( b )
Figure 4.
(
a
) V ortex pump accor ding to the open design; and (
b
) schematic illustration of the
open design.
( a ) ( b )
Figure 5. Schematic view of impellers ( a ) with curved blades; and ( b ) with straight blades.
( a ) ( b )
Figure 6. Schematic view of impellers ( a ) with winglets; and ( b ) with front shr oud.
2.3. Interim Conclusion
Overall, the cover ed design and the open design ar e based on dif fer ent assumptions about the
underlying operating principle of a vortex pump. Because it is unclear which of the two operating
principles is mainly r esponsible for the fluid transport, it is unknown which of the two design

Energies 2017 , 10 , 58 6 of 23
types should be prioritized in the first place (in terms of higher head and greater ef ficiencies).
As a consequence, it is unclear which geometric modifications ultimately optimize vortex pumps.
Regar dless of the operating principles at work, the fluid flow in the fr ont chamber can be
principally divided into two components: a through-flow and a r ecirculating flow . Figur e 7 a,b
illustrates the two flows on behalf of the cover ed design (Figure 7 a) and the open design (Figur e 7 b),
r espectively . It is an open question to what degree each component contributes to the fluid transport
and to what degr ee the two components can be separated.
( a ) ( b )
Figure 7.
(
a
) Flow model for the covered design (adapted fr om [
31
]); and (
b
) flow model for the open
design (adapted form [ 34 ]).
3. Results
3.1. Pr esentation of Data
For the pr esentation of the data, we used the values head (
H
) or corr espondingly the dimensionless
value pr essur e coef ficient (
ψ
) and the ef ficiency (
η
). The pr essur e coef ficient is a dimensionless quantity
that can be derived fr om the model laws and serves to characterize the operating behavior of a pump.
It describes the head of a pump. The pr essur e coef ficient is defined as:
ψ =
2 · g · H
π 2 · n 2 · D 2
2
(1)
with the gravitational acceleration g , the head H , the r otation speed n and the impeller diameter D 2 .
The ef ficiency is a ratio to characterize the quality of a machine. It sets the ef fective power in
r elation to the consumed power . For pumps, differ ent efficiencies can be named, as for example the
hydraulic ef ficiency or the aggr egate ef ficiency , depending on which power serves as effective power or
consumed power . In this study , we did not distinguish between authors using hydraulic efficiencies or
aggr egate ef ficiency , as none of the considered articles pr ovided any information, and it was sufficient
to determine tr ends.
Figur e 8 illustrates how the head curves, pressur e coefficient curves and the ef ficiency curves from
the primary studies wer e generated (on the left). The example shows how variations in the impeller
width af fected the head (
H
) and the pr essur e coef ficient (
ψ
; both at the top right panel) and ef ficiency
(
η
; at the bottom right panel). When integrating primary studies, first the highest ef ficiency for each
impeller width was r ead of f and ther eby defining its operation point for best ef ficiency ( BEP ). All BEP s
wer e combined into a single graph by plotting them against their respective impeller width. Finally ,
a linear tr end line was fitted thr ough all BEP s of each primary study . These steps wer e repeated for all
primary studies. This repr esentation allows displaying multiple studies in a single graph at the cost of
r educing the analyses to comparing BEP values.

Energies 2017 , 10 , 58 7 of 23
T o distinguish between the BEP s fr om differ ent design principles of vortex pumps (e.g., covered
design, open design), the following coding scheme is used for all symbol markers in the figures: gr ey-
or black-filled markers r epr esent cover ed designs of vortex pumps with semi-open impellers (e.g., [
8
]
in Figur e 8 ); cr oss markers repr esent covered designs of vortex pumps with pan impellers, either
squar e-shaped or r ound-shaped impellers (e.g., [
10
] in Figur e 8 ); black/white two-faced markers
r epr esent the open designs of vortex pumps; non-filled markers repr esent non-specified designs with
unknown impeller types (e.g., [ 5 ] in Figur e 8 ).
Figure 8. Example for the presentation of the data.
3.2. Single-Parameter Investigations
3.2.1. Impeller W idth
The impeller width r efers to the depth of the blades. Figure 9 a pictur es the head and the
pr essur e coef ficient over the impeller width. Figur e 9 b shows the efficiency at the BEP for each
vortex pumps. Generally speaking, the results suggest that a lar ger impeller width leads to greater
head and higher pr essur e coeffi cients. The r elation between the impeller width and effi ciency is not
as clear . Whereas the majority of the studies suggest the ef ficiency increases with the impeller width
incr easing, some studies [ 5 , 6 ] suggest a thr eshold for this tr end after which the ef ficiency dr ops.

Energies 2017 , 10 , 58 8 of 23
Figur e 9 a,b shows that the gradients of tr end lines dif fer between the studies. This suggests the
pr esence of the confounding influences of other design parameters. The studies differ ed in their vortex
pump design principle, but also in their specific design, for example the casing design, the volute
width, blade number , etc. That might influence the maximum r eached head and efficiency , as well,
and leads to dif fer ent tr ends and absolute values between the studies.
( a ) ( b )
Figure 9.
(
a
) Head and pressur e coefficient over impeller width; and (
b
) efficiency over impeller width.
3.2.2. Impeller Diameter
The majority of the primary studies assessed the effect of varying the impeller diameter . Overall,
these studies univocally conclude that incr easing the impeller diameter yields gr eater head and
pr essur e coef ficients. This is in accordance with insights fr om common centrifugal pumps where
similar ef fects ar e known (e.g., [
35
,
36
]). Figur e 10 a plots the head for the BEP against the impeller
diameter . Figure 10 b plots the pr essure coef ficient for the BEP against the impeller diameter . Notably ,
the gradients between the studies dif fer substantially , suggesting the presence of confounding
influences on the head characteristics. Here again, the studies differ ed in their specific design of
tested vortex pump, leading pr obably to dif fer ent tr ends and absolute values between the studies.
Figur e 11 combines the studies of Figur e 10 a,b and plots the ef ficiency for the BEP over the
impeller diameter . Overall, the trends suggest that gr eater impeller diameters lead to greater ef ficiency .
However , this tr end is not necessarily linear . The studies of Guan et al. [
2
], Zheng et al. [
5
] and
Sha et al. [ 8 ] for example suggest a U-shaped r elationship.

Energies 2017 , 10 , 58 9 of 23
( a ) ( b )
Figure 10. ( a ) Head over impeller diameter; and ( b ) pressur e coefficient over impeller diameter .
Figure 11. Efficiency over impeller diameter .
3.2.3. Number of Blades
All studies suggest that an incr eased blade number leads to gr eater pr essur e coef ficients and
gr eater ef ficiency . Figure 12 a shows the influence of the number of blades on the pr essure coef ficient
for the BEP . Figur e 12 b plots blade numbers against ef ficiency . Noteworthy , Rütschi [
1
] r eported
a decr easing ef ficiency for 12 blades. In combination with the other studies, this suggests that mor e
than 10 blades ar e not beneficial.

Energies 2017 , 10 , 58 10 of 23
( a ) ( b )
Figure 12. ( a ) Pressur e coefficient over number of blades; and ( b ) ef ficiency over number of blades.
3.3. Blade Angles
The influence of the blade angle was studied in two ways: either by changing the blade outlet
angle
β 2
at a constant blade inlet angle
β 1
or , vice versa, by changing t he blade inlet angle
β 1
at
a constant outlet angle
β 2
. Overall, increasing the outlet angle seems to incr ease the head and the
pr essur e coef ficient. Gr eater angles thus lead to mor e ef ficiency . In contrast, the transition from straight
blades to forwar d curved blades is mar ginal. Figure 13 a summarizes the influence of the blade outlet
angle
β 2
on the pr essur e coef ficient. The r esults suggest that incr easing the blade outlet angle impr oves
the pr essur e coef ficient. In particular , it is demonstrated that an impeller with an outlet angle greater
than 90
◦
(i.e., forwar d curved blades) is associated with gr eater pressur e coefficients. Figur e 13 b plots
the influence of the blade outlet angle
β 2
against ef ficiency . This shows the tendency of incr easing
ef ficiency with incr easing blade angle.
( a ) ( b )
Figure 13.
(
a
) Head and pressur e coefficient over blade outlet angle; and (
b
) efficiency over blade
outlet angle.
Guan et al. [
2
] examined the influence of varying the blade inlet angle
β 1
. Figur e 14 a shows the
r esults for head and ef ficiency that suggest increasing the inlet angle decr eases the head and slightly
the ef ficiency .

Energies 2017 , 10 , 58 11 of 23
( a ) ( b )
Figure 14.
(
a
) Head and effi ciency over blade inlet angle; and (
b
) head and effi ciency over blade
thickness to impeller diameter .
3.4. Blade Thickness
Only a single study examined the influence of varying the blade thickness [
2
]. Figure 14 b
suggests that the head and the ef ficiency of the BEP dr op with blade thickness increasing. However ,
only two configurations wer e tested.
3.5. W inglets and Fr ont Shr ouds
Jiang et al. [
12
] examined the impact of adding winglets to a semi-open impeller . The study
compar ed two dif fer ent winglet depths to an impeller without winglets. Figure 15 a shows the r esults
for head and ef ficiency over the ratio of winglet depth to impeller diameter . Overall, the head and
the ef ficiency of the impellers with winglets wer e lower than those of the impeller without winglets.
Decr easing the ratio of winglet depth to impeller diameter was associated with a lower head and
lower ef ficiency . Notably , another study by Gerlach et al. [
14
] demonstrated that adding winglets to a
vortex pump with fr ee outflow fr om the impeller (i.e., without coverage) and four curved blades led
to a gr eater head and mor e ef ficiency . On a further note, Cervinka [
24
] investigated the operation of
winglets using a numerical model. The author compar ed an impeller with winglets with a geometrically
similar impeller without winglets. The study concluded that an impeller with winglets deteriorates the
pump characteristic and its ef ficiency . These results have not been experimentally validated however ,
and they contradict the measur ement r esults of Jian et al. [ 12 ] and Gerlach et al. [ 14 ].
The maximal design of winglets r esults in a fr ont shro ud. Adding a front shr oud strongly limits
the use of vortex pumps (e.g., for pumping solid-containing fluids); however , such a modification
can pr ove insightful for understanding the principle characteristics of a vortex pump. Figure 15 b
shows the r esults for an impeller without a fr ont shr oud compar ed to an impeller with a front shr oud.
Adding the fr ont shr oud was associated with a gr eater head and mor e ef ficiency compar ed to the
semi-open impeller .

Energies 2017 , 10 , 58 12 of 23
( a ) ( b )
Figure 15.
(
a
) Head and efficiency over depth of winglet.; and (
b
) head and efficiency for impellers
with and without a front shr oud.
3.6. V olute Width
The volute width r efers to the width of side chamber gap between the casing and the impeller .
Figur e 16 a shows the head and pr essure coef ficient over the variation of volute width. All, but one
study (Sha et al. [
7
]), suggested that the head and pr essur e coef ficient decr ease when the volute width
incr eases. Figur e 16 b plots the associated ef ficiencies. Again, all but one study (Sha et al. [
7
]) suggested
that the ef ficiency decr eases when volute width increases. Each study seems to have its own optimal
ef ficiency point depending on the volute width. A parabolic curve seems to fit the measurement points
better than a linear tr end line.
( a ) ( b )
Figure 16. ( a ) Head and pressur e coefficient over volute width; and ( b ) ef ficiency over volute width.
3.7. Covering of the Impeller
The covering of the impeller r efers to the overlap between the impellers’ radial outlet and the
casing. Figur e 17 a depicts how decr easing the covering affects the head for the BEP . At zer o, the
impeller completely covers the casing. W ith increasing values, the covering decr eases until the impeller
is completely uncover ed (the maximum value for each study; e.g., 20 mm in Rütschi [
1
]). Figur e 17 a
suggests that covering the impeller decr eases the head. Figure 17 b shows the associated ef ficiencies for
the covering of the impeller . This suggests that covering the impeller decreases ef ficiency .

Energies 2017 , 10 , 58 13 of 23
( a ) ( b )
Figure 17. ( a ) Head over covering; and ( b ) efficiency over covering.
3.8. Suction Pipe Diameter
The suction pipe diameter r efers to the pipe diameter at the suction entrance of the pump.
V ariations in the suction pipe diameter only mar ginally affect the head and the pr essure coef ficient.
The ef fect of the suction pipe diameter on ef ficiency is contradictory . The studies of Sha et al. [
6
] and
Ohba et al. [
9
] show an incr ease of ef ficiency with incr easing suction pipe diameter , while the study of
Zheng et al. [ 5 ] shows the opposite behavior . Only Guan et al. [ 2 ] shows no influence of suction pipe
diameter on the efficiency . Figur e 18 a shows the results for the head and the pr essure coef ficient over
the suction pipe diameter . Figure 18 b shows the r espective values for efficiency .
( a ) ( b )
Figure 18.
(
a
) Head and pressur e coefficient over suction pipe diameter; and (
b
) efficiency over suction
pipe diameter .
3.9. Suction Pipe Inlet Geometry
Only Rütschi [
1
] examined the suction pipe inlet geometry , i.e., the design of inlet from the suction
pipe of the pump to the casing. Three variations wer e considered, shown in Figur e 19 a (fr om left
to right): a straight inlet, an inlet with a constriction and an inlet with a large radius of curvatur e.
Figur e 19 b plots the r esults of the measur ements against the head and efficiency . A straight inlet of the
suction pipe seems pr eferable in terms of highest head and efficiency . The comparisons wer e based on
an impeller with nine straight blades.

Energies 2017 , 10 , 58 14 of 23
( a ) ( b )
Figure 19.
(
a
) Differ ent inlet geometries of the suction pipes (based on [
1
]; from left): a straight inlet,
an inlet with a constriction and an inlet with a lar ge radius of curvatur e; and (
b
) influence of the suction
pipe inlet geometry on the head and efficiency .
3.10. Pr essur e Pipe Diameter
A single study tested variations in the pressur e pipe diameter by two configurations
(Zheng et al. [ 5 ]
). Figur e 20 a shows the associated head and efficiency . The r esults suggest that
a lar ge pr essur e pipe diameter decr eases the head. The impact on the efficiency is insignificant.
However , it has to be considered that only two configurations wer e tested, and correlations ar e hard
to deduce.
( a ) ( b )
Figure 20.
(
a
) Head and ef ficiency over pressur e pipe diameter; and (
b
) head and ef ficiency for differ ent
geometries of the casing.
3.11. Geometry of the Casing
The geometry of the casing refers to the specific design of the casing, for example the comparison
between a spiral casing or a ring casing. Figure 20 b shows how the geometry of the casing influences
the head and ef ficiency . The graph is based on the study of Zheng et al. [
5
]. The study compar ed
a spiral casing with a ring casing and with a half spiral casing. Both head and efficiency wer e highest
when the ring casing was used.

Energies 2017 , 10 , 58 15 of 23
3.12. Rotation Speed
As depicted in Figur e 21 a, three studies univocally suggest that higher r otation speeds lead
to gr eater head. In contrast, Figur e 21 b suggests that rotation speed has little ef fect on efficiency .
The ef fect on head r esembles insights on common centrifugal pumps for which similar ef fects have
been observed (e.g., [ 35 , 36 ]).
( a ) ( b )
Figure 21. ( a ) Head over rotation speed; and ( b ) ef ficiency over rotation speed.
3.13. Corr elations between Parameters
Some of the single primary studies explicitly deduce recommendations about specific ratios for
geometric parameters with the goal of maximizing head and/or achieving the highest efficiencies.
T able 2 pr ovides
an overview on the r ecommended ratios. W e tried to verify the suggested corr elations
based on all collected primary studies. For this pr opose, all studies were consider ed that indicated
both parameters while testing one of them. For example, the r elation between suction pipe diameter
and impeller diameter , mentioned as 0.45 by Ohba et al. [
22
] (T able 2 , last column), was tested by
looking at all single primary studies that changed the suction pipe diameter with constant impeller
diameter and vice versa. These studies were plotted over the ratio of suction pipe diameter to impeller
diameter to identify optima. However , we failed to verify the suggested correlations. This was either
because no studies tested the tar geted corr elations or the optimum itself did not exist.
T able 2. Recommended ratios for geometric parameters in articles.
Source Relationship T argeted Improvement Conclusion
Rütschi [ 1 ] b 2 /D s = (0.25–0.30) Best ef ficiencies and head Not confirmed
Ohba et al. [ 22 ] b 2 /D 2 = 0.25 Best ef ficiencies Not confirmed
Ohba et al. [ 22 ] b 4 /D 2 = 0.20 Best ef ficiencies and head Not confirmed
Zheng et al. [ 5 ] b 4 /D 2 = 0.255 Best ef ficiencies and head Not confirmed
Ohba et al. [ 22 ] D s /D 2 = 0.45 Best ef ficiencies and head Not confirmed
4. Discussion
As a major dif fer ence in the studies, the design type was highlighted, as explained at the beginning
of this paper . This is to say , in some studies, a covered design was used, a pan impeller or less common
a fr ee flow impeller . However , it is assumed that this has a significant effect on the performance,
since it possibly prevents the fr ee flow out of the impeller . A study that compares the pan impeller
with covering to a normal impeller with free outflow and without covering was partly shown by

Energies 2017 , 10 , 58 16 of 23
Rütschi [
1
]. These tested impellers ar e not dir ectly comparable due to many dif fer ent parameters,
so that a conclusion could not be drawn. However , testing such impellers, similar in parameters,
but dif fer ent by the type, would be the best way to face the assumed operating principles.
Some authors describe the optimal ratios of geometric parameters to each other to achieve the
highest head and ef ficiencies. The described optima were consider ed on the basis of the collected data
and could not be confirmed. However , it is important to note that the slopes of the suggested trends
may considerably dif fer between the primary studies. These differ ences suggest that confounding, but
unobserved factors exist that moderate the r elations between the geometric variation and the observed
behaviors. This suggests that tr ends for this type of pump might be described; however , a number of
unknown factors exist, so definite and formula-based r elationships ar e not yet grasped.
Despite the fact that volute width has been assessed in a number of studies, it often r emains
unclear how these measur ements wer e exactly implemented. The volute width could be varied,
for example, by varying the impeller widths or by moving the impeller in the casing, to change the
distance between impeller and casing. Hence, the r esults should be interpr eted with car e. The same
applies for the parameter covering. Here again, it is unclear how these experiments wer e implemented
in detail and if a change in volute width took place. Therefor e, the impact on the pump-specific
performance is not entir ely clear for this parameter , either .
Based on the data collected, it would be interesting to calculate characteristic values, such as
the specific speed or the specific diameter . This might also possibly further hint at the operating
principle of the pump. However , this was not possible because many of the studies did not fully
publish the geometry data and/or operating data or scaled them internally . Thus, no comparability
was possible. The fact to be scrutinized is that in some cases, the same measur ements were found in
various publications.
Overall, it is surprising that no literatur e works wer e found for the clogging behavior . Therefor e,
the r esults on the influence of the parameters always relate pur ely to the hydraulic data of the delivery
and do not indicate the clogging behavior . This opens up a large field of r esearch since vortex pumps
ar e actually used for the transport of fluids with solids. The same applies for the usage of back vanes
on vortex pumps. It is the practice of pump suppliers to use back vanes on vortex pump impellers,
but no studies wer e found on that. Since it is known from classical centrifugal pumps that semi-open
impellers incr ease the axial trust, it is not r eprehensible to adopt this to vortex pumps and apply back
vanes as a countermeasur e. However , this needs further clarification, since back vanes might influence
the clogging behavior .
5. Conclusions
5.1. Influence of Parameters
W e r eviewed 53 primary studies that geometrically varied the characteristics of vortex pumps and
measur ed their ef fect on the head, the pr essur e coef ficient and ef ficiency for BEP . T able 3 summarizes
these ef fects for geometric changes to the impeller . T able 4 summarizes these eff ects for geometric
changes to the casing and to the r otation speed. They show the effect of increasing a parameter on the
pump-specific characteristics head and ef ficiency for BEP . The results all apply to testing with clear
water , i.e., no clogging behavior is considered.

Energies 2017 , 10 , 58 17 of 23
T able 3. Geometric changes to the impeller and their effects on the pump-specific characteristics.
Geometric Change
by Increasing the Parameter
Effects on the Pump-Specific
Characteristics
Parameter Prefix H BEP / ψ BEP η BEP
Impeller width b 2 ↑ ↑ ↑
Impeller diameter D 2 ↑ ↑ ↑
Blade number z ↑ ↑ ↑
Blade outlet angle β 2 ↑ ↑ ↑
Blade inlet angle β 1 ↑ ↓ ↓
Blade thickness t ↑ ↓ ↓
W inglets ↑ ↑ ↑
T able 4.
Geometric changes to the casing and changes to rotation speed and their ef fects on the
pump-specific characteristics.
Geometric Change
by Increasing the Parameter
Effects on the Pump-Specific
Characteristics
Parameter Prefix H BEP / ψ BEP η BEP
V olute width b 4 ↑ ↓ ↓
Covering s ↑ ↑ ↑
Suction pipe diameter D s ↑ unambiguous unambiguous
Pressur e pipe diameter D d ↑ ↓ →
Geometry of suction pipe inlet Straight best best
Geometry of casing Ring best best
Rotation speed n ↑ ↑ →
T ables 3 and 4 summarize that incr easing the impeller width, the impeller diameter , the blade
number and the blade outlet angle all led to an incr ease of head, pressur e coefficient and ef ficiency .
However , increasing the blade inlet angle or the blade thickness r esulted in a decr ease of the head,
pr essur e coef ficient and ef ficiency . Adding winglets to the blade tips of an impeller was preferable in
terms of incr easing the head and ef ficiency compar ed to an impeller without winglets. Incr easing the
volute width led pr esumably to a decr ease of head, pressur e coefficient and ef ficiency . Incr easing the
covering pr esumably incr ease the head and ef ficiency , which means that the impeller should not be
cover ed. The influence of suction pipe diameter was unambiguous, as some studies showed that
an incr ease of suction pipe diameter led to an incr ease of head, pr essur e coef ficient and ef ficiency , but
some tr ends of studies showed the opposite. An incr ease of pr essur e pipe diameter led to a decr ease of
head. A straight design of the suction pipe inlet geometry was best in terms of head and ef ficiency
compar ed to a design with a constriction and a design with a large radius of curvatur e. Similar , a
ring casing design was best in terms of head and efficiency compar ed to a spiral casing and a half
spiral casing. An incr ease of r otation speed led to an incr ease of head, while it had little effect on
the ef ficiency .
5.2. Design Recommendations for V ortex Pumps
The single-parameter natur e of the primary studies allows drawing causal infer ences about the
ef fect of geometric changes on the pump characteristics. Therefor e, recommendations for the design of
vortex pumps can be given if r elations wer e unambiguous. W e consider r elations as unambiguous
if multiple primary studies suggest similar trends between the parameter and the head or ef ficiency .
T able 5 summarizes these design r ecommendations for the impeller , and T able 6 lists the design
r ecommendations for the casing and for the r otation speed.
Finally , it remains to clarify which operating principle is mor e likely for a vortex pump. Based on
the evaluation, the behavior is similar to a conventional centrifugal pump. A vortex pump responds to
the change in the geometry sizes in tr end with the same behavior as a conventional centrifugal pump.

Energies 2017 , 10 , 58 18 of 23
For example, the coverage of the impeller should be avoided, and the influence of diameter change
is similar . Standing out is only the parameter blade outlet angle, whereby this behavior is known by
centrifugal pumps with semi-open impellers [
37
]. Therefor e, it can be assumed that a vortex pump can
be r egar ded as a centrifugal pump with a semi-open impeller and an enlar ged side gap.
T able 5. Design recommendations for the impeller of a vortex pump.
Parameter Prefix Recommendation
Impeller width b 2 ↑
Impeller diameter D 2 ↑
Blade number z ↑
Blade outlet angle β 2 ↑
Blade inlet angle β 1 ↓
Blade thickness t ↓
W inglets - ↑
T able 6. Design recommendations for the casing and rotational speeds of a vortex pump.
Parameter Prefix Recommendation
V olute width b 4 ↓
Covering s ↑
Pressur e pipe diameter D d ↓
Geometry of suction pipe inlet - Straight
Geometry of casing - Ring
Rotation speed n ↑
Acknowledgments:
This resear ch was supported by Grundfos Holding A/S. W e thank Y ang Song and
Xue Y ousheng for assistance with the Chinese literature; Philipp Gerlach for editing the manuscript;
and Dorian Perlitz for his assistance with the graphs.
Author Contributions:
Angela Gerlach has performed the analysis and data evaluation in this paper and has
prepar ed the manuscript. Paul Uwe Thamsen, Sebastian W ulff and Christian Brix Jacobsen have consulted during
the analysis and discussion and made editorial corrections.
Conflicts of Interest: The authors declare no conflict of inter est.
Abbreviations
The following abbreviations ar e used in this manuscript:
BEP Best Efficiency Point
b 2 impeller width
b 4 volute width
D 2 impeller diameter
D s suction pipe diameter
D d pressur e pipe diameter
g gravitational acceleration
H head
n rotation speed
Q flow rate
s covering
t blade thickness
z blade number
β 1 blade inlet angle
β 2 blade outlet angle
ψ pressur e coefficient
η efficiency
Appendix A
T able A1 summarizes the geometry data of the 53 primary investigations.

Energies 2017 , 10 , 58 19 of 23
T able A1. Geometry data in the articles.
Source Assessed Parameter Design T ype D 2 (mm) b 2 (mm) z (-) b 4 (mm) β 2 ( ◦ )
b 2 —Figure 9 a,b
Rütschi [ 1 ] b 2 = 15, 20, 25, 30 mm covered nn 15, 20, 25, 30 nn nn nn
Guan et al. [ 2 ] b 2 = 30, 40, 50 mm covered 182 30, 40, 50 nn nn nn
W ang [ 4 ]-a b 2 = 30, 40, 50 mm unknown 195 30, 40, 50 nn nn nn
W ang [ 4 ]-b b 2 = 30, 40, 50 mm unknown 180 30, 40, 50 nn nn nn
Zheng et al. [ 5 ] b 2 = 14, 19, 22.5 mm unknown 100 14, 19, 22.5 nn 40.5 nn
Sha et al. [ 6 ] b 2 = 26, 28, 30 mm covered 135 26, 28, 30 8 45 nn
Sha et al. [ 7 ] b 2 = 35, 40 mm covered 232 35, 40 10 100 nn
Sha et al. [ 8 ] b 2 = 50, 55, 60, 65 mm covered 286 50, 55, 60, 65 8 68 nn
Ohba et al. [ 9 ] b 2 = 30, 40, 50, 60 mm covered, pan impeller 265 30, 40, 50, 60 nn 100 nn
Masanori [ 10 ] b 2 = 19.95, 40.5 mm covered, pan impeller 300 19.95, 40.5 10 nn 90
D 2 —Figures 10 a,b and 11
Rütschi [ 1 ] D 2 = 200, 210, 220, 230, 240, 250 mm cover ed 200, 210, 220, 230, 240, 250 nn nn nn nn
Guan et al. [ 2 ] D 2 = 115, 125, 135, 140 mm cover ed 115, 125, 135, 140 nn nn nn nn
W ang [ 4 ]-c D 2 = 170, 180, 195 mm unknown 170, 180, 195 50 nn nn nn
W ang [ 4 ]-d D 2 = 170, 180, 195 mm unknown 170, 180, 195 30 nn nn nn
Zheng et al. [ 5 ] D 2 = 90, 100, 118 mm unknown 90, 100, 118 nn nn nn nn
Sha et al. [ 6 ] D 2 = 125, 135, 140 mm covered 125, 135, 140 30 8 45 nn
Sha et al. [ 7 ] D 2 = 125, 135, 140 mm covered 125, 135, 140 26 7 40 nn
Sha et al. [ 8 ] D 2 = 125, 135, 140 mm unknown 125, 135, 140 32 8 45 nn
Ohba et al. [ 9 ]-a D 2 = 195, 265 mm covered 195, 265 25 nn 100 nn
Ohba et al. [ 9 ]-b D 2 = 195, 265 mm covered 195, 265 25 nn 50 nn
Lubieniecki [ 11 ]-a D 2 = 381, 431.8, 457.2 mm covered 381, 431.8, 457.2 76.2 nn nn 90
Lubieniecki [ 11 ]-b D 2 = 381, 431.8, 457.2 mm covered 381, 431.8, 457.2 50.8 nn nn 45
Lubieniecki [ 11 ]-c D 2 = 381, 431.8, 457.2 mm covered 381, 431.8, 457.2 38.1 nn nn 45
z—Figure 12 a,b
Rütschi [ 1 ] z = 6, 8, 9, 12 covered nn nn 6, 8, 9, 12 nn nn
Guan et al. [ 2 ] z = 6, 8, 10 covered 98 nn 6, 8, 10 nn 90
Masanori [ 10 ] z = 6,10 covered, pan impeller 300 40.05 6, 10 nn 90
β 2 —Figure 13 a,b
Guan et al. [ 2 ] β 2 = 30 ◦ , 90 ◦ covered 182 nn 7 nn 30, 90
Sha et al. [ 6 ] β 2 = 45 ◦ , 90 ◦ , 135 ◦ covered 105 30 8 45 45, 90, 135

Energies 2017 , 10 , 58 20 of 23
T able A1. Cont.
Source Assessed Parameter Design T ype D 2 (mm) b 2 (mm) z (-) b 4 (mm) β 2 ( ◦ )
Sha et al. [ 8 ] β 2 = 45 ◦ , 90 ◦ , 135 ◦ covered 105 23 7 45 45, 90, 135
Masanori [ 10 ] β 2 = 30 ◦ , 90 ◦ covered, pan impeller 300 40.05 10 nn 30, 90
β 1 —Figure 14 a
Guan et al. [ 2 ] β 2 = 30, 90 ◦ covered 300 40.05 10 nn 30, 90
t—Figure 14 b
Guan et al. [ 2 ] t /D 2 = 0.02, 0.05 covered 98 nn nn nn nn
W inglets—Figure 15 a
Jiang et al. [ 12 ] Depth of winglets covered nn nn nn nn nn
Front shroud—Figure 15 b
Zheng et al. [ 5 ] W ith and without fr ont shroud unknown nn 13 7 30.1 nn
Gerlach et al. [ 14 ] W ith and without fr ont shroud open 230 nn 4 80 nn
b 4 —Figure 16 a,b
Zheng et al. [ 5 ] b 4 = 25.5, 35.5, 44 mm unknown nn nn nn 25.5, 35.5, 44 nn
Sha et al. [ 6 ] b 4 = 50, 56, 62 mm covered 200 40 8 50, 56, 62 nn
Sha et al. [ 7 ] b 4 = 80, 100, 125 mm covered 268 50 8 80, 100, 125 nn
Sha et al. [ 8 ] b 4 = 80, 100, 125 mm covered 328 42 8 52, 60, 68 nn
Ohba et al. [ 9 ] b 4 = 34, 50, 76 mm covered, pan impeller 265 25 nn 34, 50, 76 nn
Covering—Figure 17 a,b
Rütschi [ 1 ]-a s = 0, 20 mm covered nn nn 6 nn 90
Rütschi [ 1 ]-b s = 0, 20 mm cover ed nn nn 12 nn 90
Sha and Hou [ 16 ] s = 0, 3, 6, 8 mm covered 94 20 8 25 90
D s —Figure 18 a,b
Guan et al. [ 2 ] D s = 45, 55, 65 mm covered 100 nn nn nn nn
Zheng et al. [ 5 ] D s = 49, 60 mm unknown 93.4 22.5 8 40 nn
Sha et al. [ 6 ] D s = 50, 55, 60, 65 mm covered 105 30 8 45 nn
Ohba et al. [ 9 ] D s = 53, 80, 104, 131 mm covered, pan impeller 265 25 nn 50 nn
Geometry suction pipe—Figure 19 b
Rütschi [ 1 ] Inlet straight, constriction, large radius unknown nn nn 9 nn 90

Energies 2017 , 10 , 58 21 of 23
T able A1. Cont.
Source Assessed Parameter Design T ype D 2 (mm) b 2 (mm) z (-) b 4 (mm) β 2 ( ◦ )
D d —Figure 20 a
Zheng et al. [ 5 ] D d = 50, 80 mm unknown nn nn nn nn nn
Geometry casing— Figure 20 b
Zheng et al. [ 5 ] Spiral, Ring, half Spiral unknown 93.4 22.5 nn nn nn
n—Figure 21 a,b
Li and Feng [ 17 ]-a n = 800, 1000, 1200 min − 1 covered 150 45 6 50 90
Li and Feng [ 17 ]-b n = 1000, 1200, 1300 min − 1 covered 150 35 9 50 90
Sha and Bai [ 18 ] n = 2200, 2400, 2600, 2800, 2850, 2900 min − 1 unknown 96 22 8 25 90

Energies 2017 , 10 , 58 22 of 23
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