Abstract

A local loss analysis (LLA) based on entropy production is presented for the numerical three-dimensional (3D) simulation of isothermal centrifugal pump flow. A finite volume method and a statistical turbulence model are employed. Wall functions for direct and turbulent entropy production in isothermal flow are derived, implemented in a node-centered finite volume scheme as a postprocessing procedure, and validated on an attached channel flow as well as on separated flow in an asymmetric diffuser. The integrity of the entropy wall function is demonstrated by a loss balance for a wide range of boundary layer resolution in terms of nondimensional wall distance y+1 to 200. Remaining differences to the total pressure loss are traced back to the particular turbulent wall function for the flow solution within the finite volume solver and vanish toward a wall resolution of the viscous sublayer, i.e., y+1. LLA together with the new entropy wall function is applied to highly unsteady isothermal flow in a single-blade pump as well as to part-load operation of a conventional multiblade pump which reveals distinctive flow structures that are associated with entropy production. By these examples, it is demonstrated how efficiency characteristics of centrifugal pumps can be attributed to local loss production in particular flow regions.

References

References
1.
Herwig
,
H.
, and
Kock
,
F.
,
2006
, “
Direct and Indirect Methods of Calculating Entropy Generation Rates in Turbulent Convective Heat Transfer Problems
,”
Heat Mass Transfer
,
43
(
3
), pp.
207
215
.10.1007/s00231-006-0086-x
2.
Bejan
,
A.
,
1979
, “
A Study of Entropy Generation in Fundamental Convective Heat Transfer
,”
ASME J. Heat Transfer
,
101
(
4
), pp.
718
725
.10.1115/1.3451063
3.
Bejan
,
A.
,
1980
, “
Second Law Analysis in Heat Transfer
,”
Energy
,
5
(
8–9
), pp.
720
732
.10.1016/0360-5442(80)90091-2
4.
Bejan
,
A.
, and
Kestin
,
J.
,
1983
,
Entropy Generation Through Heat and Fluid Flow
,
Wiley
, Boulder, CO.
5.
Kock
,
F.
,
2003
, “
Bestimmung Der Lokalen Entropieproduktion in Turbulenten Strömungen Und Deren Nutzung Zur Bewertung Konvektiver Transportprozesse
,” Ph.D. thesis,
Technischen Universität Hamburg-Harburg
,
Hamburg, Germany
.
6.
Kock
,
F.
, and
Herwig
,
H.
,
2004
, “
Local Entropy Production in Turbulent Shear Flows: A high-Reynolds Number Model With Wall Functions
,”
Int. J. Heat Mass Transfer
,
47
(
10–11
), pp.
2205
2215
.10.1016/j.ijheatmasstransfer.2003.11.025
7.
Kock
,
F.
, and
Herwig
,
H.
,
2005
, “
Entropy Production Calculation for Turbulent Shear Flows and Their Implementation in CFD Codes
,”
Int. J. Heat Fluid Flow
,
26
(
4
), pp.
672
680
.10.1016/j.ijheatfluidflow.2005.03.005
8.
Böhle
,
M.
,
Fleder
,
A.
, and
Mohr
,
M.
,
2016
, “
Study of the Losses in Fluid Machinery With the Help of Entropy
,”
International Symposium on Transport Phenomena and Dynamics of Rotating Machinery
, Honolulu, HI, Apr. 10–15, p.
9
.http://isromac-isimet.univ-lille1.fr/upload_dir/finalpaper/86.f14-4-3_isromac16.pdf
9.
Li
,
X.
,
Zhu
,
Z.
,
Li
,
Y.
, and
Chen
,
X.
,
2016
, “
Experimental and Numerical Investigations of Head-Flow Curve Instability of a Single-Stage Centrifugal Pump With Volute Casing
,”
Proc. Inst. Mech. Eng., Part A: J. Power Energy
,
230
(
7
), pp.
633
647
.10.1177/0957650916663326
10.
Pei
,
J.
,
Meng
,
F.
,
Li
,
Y.
,
Yuan
,
S.
, and
Chen
,
J.
,
2016
, “
Effects of Distance Between Impeller and Guide Vane on Losses in a Low Head Pump by Entropy Production Analysis
,”
Adv. Mech. Eng.
,
8
(
11
), pp.
1
11
.10.1177/1687814016679568
11.
Li
,
D.
,
Gong
,
R.
,
Wang
,
H.
,
Xiang
,
G.
,
Wei
,
X.
, and
Qin
,
D.
,
2016
, “
Entropy Production Analysis for Hump Characteristics of a Pump Turbine Model
,”
Chin. J. Mech. Eng.
,
29
(
4
), pp.
803
812
.10.3901/CJME.2016.0414.052
12.
Cao
,
J.
,
Pei
,
J.
,
Gu
,
Y.
,
Wang
,
W.
, and
Yuan
,
S.
,
2019
, “
Flow Losses Analysis in a Mixed Flow Pump With Annular Volute by Entropy Production Evaluation
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
240
(
3
), p.
032047
.10.1088/1755-1315/240/3/032047
13.
Koranteng Osman
,
M.
,
Wang
,
W.
,
Yuan
,
J.
,
Zhao
,
J.
,
Wang
,
Y.
, and
Liu
,
J.
,
2019
, “
Flow Loss Analysis of a Two-Stage Axially Split Centrifugal Pump With Double Inlet Under Different Channel Designs
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
233
(
15
), pp.
5316
5328
.10.1177/0954406219843573
14.
Zhao
,
X.
,
Luo
,
Y.
,
Wang
,
Z.
,
Xiao
,
Y.
, and
Avellan
,
F.
,
2019
, “
Unsteady Flow Numerical Simulations on Internal Energy Dissipation for a Low-Head Centrifugal Pump at Part-Load Operating Conditions
,”
Energies
,
12
(
10
), p.
2013
.10.3390/en12102013
15.
Okamura
,
T.
,
1980
, “
Radial Thrust in Centrifugal Pumps With a Single-Vane Impellers
,”
Bull. JSME
,
23
(
180
), pp.
895
901
.10.1299/jsme1958.23.895
16.
Aoki
,
M.
,
1984
, “
Instantaneous Interblade Pressure Distributions and Fluctuating Radial Thrust in a Single-Blade Centrifugal Pump
,”
Bull. JSME
,
27
(
233
), pp.
2413
2420
.10.1299/jsme1958.27.2413
17.
Benra
,
F.-K.
,
Dohmen
,
H.-J.
, and
Sommer
,
M.
,
2006
, “
Flow Field Visualization of a Single-Blade Centrifugal Pump Using PIV-Method-Comparison to Numerical Results
,”
J. Visualization
,
9
(
4
), pp.
358
358
.10.1007/BF03181771
18.
Daly
,
J.
,
De Souza
,
B.
,
Niven
,
A.
, and
Frawley
,
P.
,
2006
, “
Numerical Simulation of Transient Flow and Head Distribution Through a Single Blade Centrifugal Pump Impeller
,” Proceedings of the
Fourth WSEAS International Conference on Fluid Mechanics and Aerodynamics
, Elounda, Greece, Aug. 21–23, pp.
343
348
.
19.
Zwingenberg
,
M.
, and
Benra
,
F. K.
,
2006
, “
Measurement of the Periodic Unsteady Flow in a Single-Blade Centrifugal Pump by PIV-Method
,”
Proceedings of the Fourth WSEAS International Conference on Fluid Mechanics and Aerodynamics
, Elounda, Greece, Aug. 21–23, pp.
325
330
.
20.
Savilius
,
N.
, and
Benra
,
F. K.
,
2006
, “
Experimental Investigation of Transient Hydrodynamic Forces of a Single-Blade Centrifugal Pump
,”
Proceedings of the 4th WSEAS International Conference on Fluid Mechanics and Aerodynamics
, Elounda, Greece, Aug. 21–23, pp.
331
336
.
21.
Pei
,
J.
,
Yuan
,
S.
,
Yuan
,
J.
, and
Wang
,
W.
,
2013
, “
The Influence of the Flow Rate on Periodic Flow Unsteadiness Behaviors in a Sewage Centrifugal Pump
,”
J. Hydrodyn., Ser. B
,
25
(
5
), pp.
702
709
.10.1016/S1001-6058(13)60415-1
22.
Melzer
,
S.
,
Müller
,
T.
,
Schepeler
,
S.
,
Kalkkuhl
,
T.
, and
Skoda
,
R.
,
2019
, “
Experimental and Numerical Investigation of the Transient Characteristics and Volute Casing Wall Pressure Fluctuations of a Single-Blade Pump
,”
Proc. Inst. Mech. Eng., Part E: J. Process Mech. Eng.
,
233
(
2
), pp.
280
291
.10.1177/0954408918780524
23.
Melzer
,
S.
,
Schepeler
,
S.
,
Förster
,
J.
,
Friderich
,
J.
,
Kalkkuhl
,
T.
, and
Skoda
,
R.
,
2019
, “
Experimental Investigation of Transient Characteristics of Single-Blade and Two-Blade Pumps
,”
13th European Conference on Turbomachinery Fluid Dynamics and Thermodynamics
, Lausanne, Switzerland, Apr. 8–12, p.
12
.10.29008/ETC2019-076
24.
Japikse
,
D.
,
Marscher
,
W. D.
, and
Furst
,
R. B.
,
1997
,
Centrifugal Pump Design and Performance
,
Concepts ETI
, White River Junction, VT.
25.
Chu
,
S.
,
Dong
,
R.
, and
Katz
,
J.
,
1995
, “
Relationship Between Unsteady Flow, Pressure Fluctuations, and Noise in a Centrifugal Pump - Part B: Effects of Blade-Tongue Interactions
,”
ASME J. Fluids Eng.
,
117
(
1
), pp.
30
35
.10.1115/1.2816814
26.
Zhang
,
M.
, and
Tsukamoto
,
H.
,
2005
, “
Unsteady Hydrodynamic Forces Due to Rotor-Stator Interaction on a Diffuser Pump With Identical Number of Vanes on the Impeller and Diffuser
,”
ASME J. Fluids Eng.
,
127
(
4
), pp.
743
751
.10.1115/1.1949640
27.
Barrio
,
R.
,
Blanco
,
E.
,
Parrondo
,
J.
,
González
,
J.
, and
Fernández
,
J.
,
2008
, “
The Effect of Impeller Cutback on the Fluid-Dynamic Pulsations and Load at the Blade-Passing Frequency in a Centrifugal Pump
,”
ASME J. Fluids Eng.
,
130
(
11
), p.
11
.10.1115/1.2969273
28.
Barrio
,
R.
,
Parrondo
,
J.
, and
Blanco
,
E.
,
2010
, “
Numerical Analysis of the Unsteady Flow in the Near-Tongue Region in a Volute-Type Centrifugal Pump for Different Operating Points
,”
Comput. Fluids
,
39
(
5
), pp.
859
870
.10.1016/j.compfluid.2010.01.001
29.
Spence
,
R.
, and
Amaral-Teixeira
,
J.
,
2009
, “
A CFD Parametric Study of Geometrical Variations on the Pressure Pulsations and Performance Characteristics of a Centrifugal Pump
,”
Comput. Fluids
,
38
(
6
), pp.
1243
1257
.10.1016/j.compfluid.2008.11.013
30.
Si
,
Q.
,
Yuan
,
J.
,
Yuan
,
S.
,
Wang
,
W.
,
Zhu
,
L.
, and
Bois
,
G.
,
2014
, “
Numerical Investigation of Pressure Fluctuation in Centrifugal Pump Volute Based on SAS Model and Experimental Validation
,”
Adv. Mech. Eng.
,
6
, p.
972081
.10.1155/2014/972081
31.
Casimir
,
N.
,
Xiangyuan
,
Z.
,
Ludwig
,
G.
, and
Skoda
,
R.
,
2019
, “
Assessment of Statistical Eddy-Viscosity Turbulence Models for Unsteady Flow at Part and Overload Operation of Centrifugal Pumps
,”
13th European Conference on Turbomachinery Fluid Dynamics and Thermodynamics
, Lausanne, Switzerland, Apr. 8–12, p.
13
.https://www.euroturbo.eu/publications/proceedings-papers/etc2019-047/
32.
Casimir
,
N.
,
Zhu
,
X.
,
Hundshagen
,
M.
,
Ludwig
,
G.
, and
Skoda
,
R.
,
2020
, “
Numerical Study of Rotor-Stator Interaction of a Centrifugal Pump at Part Load With Special Emphasis on Unsteady Blade Load
,”
ASME J. Fluids Eng.
,
142
(
8
), p.
14
.10.1115/1.4046622
33.
Spurk
,
J. H.
, and
Aksel
,
N.
,
2010
,
Strömungsmechanik - Einführung in Die Theorie Der Strömung
, Vol.
8
,
Springer
, Berlin.
34.
Wilcox
,
D. C.
,
1993
,
Turbulence Modelling for CFD
,
DCW Industries
, La Canada, USA.
35.
Mathieu
,
J.
, and
Scott
,
J.
,
2000
,
An Introduction to Turbulent Flow
,
Cambridge University Press
, Cambridg, United Kingdom.
36.
Moore
,
J.
, and
Moore
,
J. G.
,
1983
, “
Entropy Production Rates From Viscous Flow Calculations—Part I: A Turbulent Boundary Layer Flow
,”
ASME
Paper No. 83-GT-70.10.1115/83-GT-70
37.
Ferziger
,
J. H.
, and
Perić
,
M.
,
2002
,
Computational Methods for Fluid Dynamics
, Vol.
3
,
Springer
, Heidelberg, Germany.
38.
Gersten
,
K.
, and
Herwig
,
H.
,
1992
,
Strömungsmechanik—Grundlagen Der Impuls-, Wärme- Und Stoffübertragung Aus Asymptotischer Sicht
, Vol.
6
,
Springer
, Wiesbaden, Germany.
39.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.10.2514/3.12149
40.
Steinbrecher
,
C.
,
Skoda
,
R.
,
Schilling
,
R.
,
Müller
,
N.
,
Breitenbach
,
A.
, and
Mendler
,
N.
,
2003
, “
Numerical Simulation of a Self-Stabilizing Rotor of a Centrifugal Pump
,”
ASME
Paper No. FEDSM2003-45468.10.1115/FEDSM2003-45468
41.
Skoda
,
R.
,
Schilling
,
R.
, and
Schobeiri
,
M. T.
,
2007
, “
Numerical Simulation of the Transitional and Unsteady Flow Through a Low Pressure Turbine
,”
Int. J. Rotating Mach.
,
2007
, pp.
1
11
.10.1155/2007/10940
42.
Mottyll
,
S.
, and
Skoda
,
R.
,
2016
, “
Numerical 3D Flow Simulation of Ultrasonic Horns With Attached Cavitation Structures and Assessment of Flow Aggressiveness and Cavitation Erosion Sensitive Wall Zones
,”
Ultrason. Sonochem.
,
31
, pp.
570
589
.10.1016/j.ultsonch.2016.01.025
43.
Moser
,
R. D.
,
Kim
,
J.
, and
Mansour
,
N. N.
,
1999
, “
Direct Numerical Simulation of Turbulent Channel Flow Up to Re τ = 590
,”
Phys. Fluids
,
11
(
4
), pp.
943
945
.10.1063/1.869966
44.
Baehr
,
H. D.
, and
Kabelac
,
S.
,
2016
,
Thermodynamik
, Vol.
16
,
Springer
, Berlin.
45.
Menter
,
F.
, and
Esch
,
T.
,
2001
, “
Elements of Industrial Heat Transfer Prediction
,”
16th Brazilian Congress of Mechanical Engineering
, Uberlandia, Minas Gerias, Brasil, Nov. 21–30, pp.
117
127
.
46.
Vieser
,
W.
,
Esch
,
T.
, and
Menter
,
F.
,
2002
, “
Heat Transfer Predictions Using Advanced Two-Equation Turbulence Models
,” CFX, Wallingford, CT, Report No. CFX-VAL10/0602.
47.
Kalitzin
,
G.
,
Medic
,
G.
,
Iaccarino
,
G.
, and
Durbin
,
P.
,
2005
, “
Near-Wall Behavior of RANS Turbulence Models and Implications for Wall Functions
,”
J. Comput. Phys.
,
204
(
1
), pp.
265
291
.10.1016/j.jcp.2004.10.018
48.
Obi
,
S.
,
Aoki
,
K.
, and
Masuda
,
S.
,
1993
, “
Experimental and Computational Study of Turbulent Separating Flow in an Asymmetric Plane Diffuser
,”
Ninth Symposium on Turbulent Shear Flows
, Hyoto, Japan, Aug. 16–18, p.
4
.
49.
Buice
,
C. U.
, and
Eaton
,
J. K.
,
2000
, “
Experimental Investigation of Flow Through an Asymmetric Plane Diffuser
,”
ASME J. Fluids Eng.
,
122
(
2
), pp.
433
435
.10.1115/1.483278
50.
Skoda
,
R.
,
Schilling
,
R.
,
Thurso
,
J.
, and
Stoffel
,
B.
,
2002
, “
Numerical Simulation of Unsteady and Transitional Flows Pertaining to Turbine Cascades
,”
Eng. Turbul. Modell. Exp.
, 5, pp.
759
768
.10.1016/B978-008044114-6/50073-9
51.
Menter
,
F. R.
,
Kuntz
,
M.
, and
Langtry
,
R.
,
2003
, “
Ten Years of Industrial Experience With the SST Turbulence Model
,”
Turbul. Heat Mass Transfer
,
4
(
1
), pp.
625
632
.https://cfd.spbstu.ru/agarbaruk/doc/2003_Menter,%20Kuntz,%20Langtry_Ten%20years%20of%20industrial%20experience%20with%20the%20SST%20turbulence
52.
Davidson
,
L.
,
2006
, “
Evaluation of the SST-SAS Model: Channel Flow, Asymmetric Diffuser and Axi-Symmetric Hill
,”
European Conference on Computational Fluid Dynamics
, Egmond aan Zee, The Netherlands, Sept. 5–8, p.
20
.https://repository.tudelft.nl/islandora/object/uuid%3A5d23e2a6-5675-450d-bf3d-1dd40d736cae
53.
Melzer
,
S.
,
Schepeler
,
S.
,
Kalkkuhl
,
T.
, and
Skoda
,
R.
,
2019
, “
Experimental Analysis of Transient Flow Characteristics and Impeller Deflection in Single-Blade and Two-Blade Pumps
,”
Fourth International Rotating Equipment Conference
, Wiesbaden, Germany, Sept. 24–25.
54.
Melzer
,
S.
,
Munsch
,
P.
,
Förster
,
J.
,
Friderich
,
J.
, and
Skoda
,
R.
,
2020
, “
A System for Time-Fluctuating Flow Rate Measurements in a Single-Blade Pump Circuit
,”
Flow Meas. Instrum.
,
71
, p.
101675
.10.1016/j.flowmeasinst.2019.101675
55.
Meschkat
,
S.
, and
Stoffel
,
2002
, “
The Local Impeller Head at Different Circumferential Positions in a Volute Casing Centrifugal Pump in Comparison to the Characteristic Curve of the Impeller Alone
,”
21st IAHR Symposium
, Lausanne, Switzerland, Sept. 9–12.
56.
Hergt
,
P.
,
Meschkat
,
S.
, and
Stoffel
,
B.
,
2004
, “
The Flow and Head Distribution Within the Volute of a Centrifugal Pump in Comparison With the Characteristics of the Impeller Without Casing
,”
Modelling Fluid Flow
,
Springer
, Berlin, pp.
407
418
.
57.
Meschkat
,
S.
,
2004
, “
Experimentelle Untersuchung Der Auswirkungen Instationärer Rotor-Stator-Wechselwirkungen Auf Das Betriebsverhalten Einer Spiralgehäusepumpe
,” Ph.D. thesis,
Technische Universität Darmstadt, Darmstadt, Germany
.
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