Abstract

In recent optical flow experiments on a transparent volute-type radial centrifugal pump, an accumulation of air bubbles to adherent gas pockets within the impeller blade channels was observed. A transition of unsteady bubbly flow toward an attached gas pocket at the blade suction side was found for increasing air loading of the liquid water phase. This steadily attached pocket shows a distinctive unsteady wake. A reproduction of the transition from bubbly to pocket flow in a three-dimensional (3D) flow simulation demands the treatment of dispersed bubbly flow, on the one hand, and of coherent air regions, on the other hand. Therefore, a hybrid flow solver is adopted based on an Euler–Euler two-fluid (EE2F) method for dispersed flows and features volume-of-fluid (VOF) properties when air accumulations form. A scale-adaptive simulation (SAS) turbulence model is utilized to account for highly unsteady flow regions. For the time being, a monodisperse bubble size distribution is assumed for the dispersed part of the flow. For an operation range close to the design point and rising air loading, the flow transition from bubbly to pocket flow is well captured by the hybrid simulation method. Even an alternating pocket flow in between bubbly and pocket flow regime is predicted. The simulation method is still limited by an appropriate choice of a monodisperse bubble diameter. Therefore, the disperse model part of the hybrid flow solver will be coupled with population balance and bubble interaction models in future studies.

References

1.
Chan
,
A.
,
Kawaji
,
M.
,
Nakamura
,
H.
, and
Kukita
,
Y.
,
1999
, “
Experimental Study of Two-Phase Pump Performance Using a Full Size Nuclear Reactor Pump
,”
Nucl. Eng. Des.
,
193
(
1–2
), pp.
159
172
.10.1016/S0029-5493(99)00150-8
2.
Amoresano
,
A.
,
Langella
,
G.
,
Niola
,
V.
, and
Quaremba
,
G.
,
2014
, “
Advanced Image Analysis of Two-Phase Flow Inside a Centrifugal Pump
,”
Adv. Mech. Eng.
,
6
(
1
), p.
958320
.10.1155/2014/958320
3.
Cappelino
,
C. A.
,
Roll
,
D. R.
, and
Wilson
,
G.
,
1992
, “
Design Considerations and Application Guidelines for Pumping Liquids With Entrained Gas Using Open Impeller Centrifugal Pump
,”
Int. Pump User Symp.
,
9
, pp.
51
60
.10.21423/R1T11F
4.
Monte Verde
,
W.
,
Biazussi
,
J. L.
,
Sassim
,
N. A.
, and
Bannwart
,
A. C.
,
2017
, “
Experimental Study of Gas-Liquid Two-Phase Flow Patterns Within Centrifugal Pumps Impellers
,”
Exp. Therm. Fluid Sci.
,
85
, pp.
37
51
.10.1016/j.expthermflusci.2017.02.019
5.
Mansour
,
M.
,
Wunderlich
,
B.
, and
Thévenin
,
D.
,
2018
, “
Effect of Tip Clearance Gap and Inducer on the Transport of Two-Phase Air-Water Flows by Centrifugal Pumps
,”
Exp. Therm. Fluid Sci.
,
99
, pp.
487
509
.10.1016/j.expthermflusci.2018.08.018
6.
Mansour
,
M.
,
Wunderlich
,
B.
, and
Thévenin
,
D.
,
2018
, “
Experimental Study of Two-Phase Air/Water Flow in a Centrifugal Pump Working With a Closed or a Semi-Open Impeller
,”
ASME
Paper No. GT2018-75380.10.1115/GT2018-75380
7.
Sato
,
S.
,
Furukawa
,
A.
, and
Takamatsu
,
Y.
,
1996
, “
Air-Water Two-Phase Flow Performance of Centrifugal Pump Impellers With Various Blade Angles
,”
JSME Int. J., Ser. B
,
39
(
2
), pp.
223
229
.10.1299/jsmeb.39.223
8.
Liao
,
M.
,
Si
,
Q.
,
Fan
,
M.
,
Wang
,
P.
,
Liu
,
Z.
,
Yuan
,
S.
,
Cui
,
Q.
, and
Bois
,
G.
,
2021
, “
Experimental Study on Flow Behavior of Unshrouded Impeller Centrifugal Pumps Under Inlet Air Entrainment Condition
,”
Int. J. Turbomach. Propul. Power
,
6
(
3
), p.
31
.10.3390/ijtpp6030031
9.
Schäfer
,
T.
,
Neumann-Kipping
,
M.
,
Bieberle
,
A.
,
Bieberle
,
M.
, and
Hampel
,
U.
,
2020
, “
Ultrafast X-Ray Computed Tomography Imaging for Hydrodynamic Investigations of Gas–Liquid Two-Phase Flow in Centrifugal Pumps
,”
ASME J. Fluids Eng.
,
142
(
4
), p.
041502
.10.1115/1.4045497
10.
Neumann
,
M.
,
Schäfer
,
T.
,
Bieberle
,
A.
, and
Hampel
,
U.
,
2016
, “
An Experimental Study on the Gas Entrainment in Horizontally and Vertically Installed Centrifugal Pumps
,”
ASME J. Fluids Eng.
,
138
(
9
), p.
091301
.10.1115/1.4033029
11.
Mansour
,
M.
,
Kováts
,
P.
,
Wunderlich
,
B.
, and
Thévenin
,
D.
,
2018
, “
Experimental Investigations of a Two-Phase Gas/Liquid Flow in a Diverging Horizontal Channel
,”
Exp. Therm. Fluid Sci.
,
93
, pp.
210
217
.10.1016/j.expthermflusci.2017.12.033
12.
Mansour
,
M.
,
Parikh
,
T.
, and
Thévenin
,
D.
,
2020
, “
Influence of the Shape of the Impeller Blade Trailing Edge on Single and Two-Phase Air Water Flows in a Centrifugal Pump
,”
Proceedings of Turbomachinery & Pump Symposia
, Houston, TX, Dec. 13–16.
13.
Mansour
,
M.
,
Kopparthy
,
S.
, and
Thévenin
,
D.
,
2022
, “
Investigations on the Effect of Rotational Speed on the Transport of Air-Water Two-Phase Flows by Centrifugal Pumps
,”
Int. J. Heat Fluid Flow
,
94
, p.
108939
.10.1016/j.ijheatfluidflow.2022.108939
14.
Stel
,
H.
,
Ofuchi
,
E. M.
,
Alves
,
R. F.
,
Chiva
,
S.
, and
Morales
,
R. E. M.
,
2020
, “
Experimental Analysis of Gas–Liquid Flows in a Centrifugal Rotor
,”
ASME J. Fluids Eng.
,
142
(
3
), p.
031101
.10.1115/1.4045857
15.
Shao
,
C.
,
Li
,
C.
, and
Zhou
,
J.
,
2018
, “
Experimental Investigation of Flow Patterns and External Performance of a Centrifugal Pump That Transports Gas-Liquid Two-Phase Mixtures
,”
Int. J. Heat Fluid Flow
,
71
, pp.
460
469
.10.1016/j.ijheatfluidflow.2018.05.011
16.
Parikh
,
T.
,
Mansour
,
M.
, and
Thévenin
,
D.
,
2020
, “
Investigations on the Effect of Tip Clearance Gap and Inducer on the Transport of Air-Water Two-Phase Flow by Centrifugal Pumps
,”
Chem. Eng. Sci.
,
218
, p.
115554
.10.1016/j.ces.2020.115554
17.
Pineda
,
H.
,
Biazussi
,
J.
,
López
,
F.
,
Oliveira
,
B.
,
Carvalho
,
R. D.
,
Bannwart
,
A. C.
, and
Ratkovich
,
N.
,
2016
, “
Phase Distribution Analysis in an Electrical Submersible Pump (ESP) Inlet Handling Water–Air Two-Phase Flow Using Computational Fluid Dynamics (CFD)
,”
J. Pet. Sci. Eng.
,
139
, pp.
49
61
.10.1016/j.petrol.2015.12.013
18.
Zhu
,
J.
,
Zhu
,
H.
,
Zhang
,
J.
, and
Zhang
,
H.-Q.
,
2019
, “
A Numerical Study on Flow Patterns Inside an Electrical Submersible Pump (ESP) and Comparison With Visualization Experiments
,”
J. Pet. Sci. Eng.
,
173
, pp.
339
350
.10.1016/j.petrol.2018.10.038
19.
De Santis
,
A.
,
Colombo
,
M.
,
Hanson
,
B. C.
, and
Fairweather
,
M.
,
2021
, “
A Generalized Multiphase Modelling Approach for Multiscale Flows
,”
J. Comput. Phys.
,
436
, p.
110321
.10.1016/j.jcp.2021.110321
20.
Hundshagen
,
M.
,
Rave
,
K.
,
Mansour
,
M.
,
Thévenin
,
D.
, and
Skoda
,
R.
,
2021
, “
Assessment of Multi-Phase CFD Methods for Gas-Laden Liquid Flows in Centrifugal Pumps With Particular Emphasis on the Change of Flow Morphology
,”
Proceeding of 14th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics
, Gdansk, Poland, Apr. 12–16, Paper No. ETC2021-529.10.29008/ETC2021-529
21.
Si
,
Q.
,
Bois
,
G.
,
Zhang
,
K.
, and
Yuan
,
J.
,
2017
, “
Air-Water Two-Phase Flow Experimental and Numerical Analysis in a Centrifugal Pump
,”
Proceedings of 12th European Conference on Turbomachinery Fluid Dynamics & Thermodynamics
, Stockholm, Sweden, Apr. 3–7, Paper No. ETC2017-054.10.29008/ETC2017-054
22.
Si
,
Q.
,
Bois
,
G.
,
Jiang
,
Q.
,
He
,
W.
,
Ali
,
A.
, and
Yuan
,
S.
,
2018
, “
Investigation on the Handling Ability of Centrifugal Pumps Under Air–Water Two-Phase Inflow: Model and Experimental Validation
,”
Energies
,
11
(
11
), p.
3048
.10.3390/en11113048
23.
Si
,
Q.
,
Bois
,
G.
,
Liao
,
M.
,
Zhang
,
H.
,
Cui
,
Q.
, and
Yuan
,
S.
,
2019
, “
A Comparative Study on Centrifugal Pump Designs and Two-Phase Flow Characteristic Under Inlet Gas Entrainment Conditions
,”
Energies
,
13
(
1
), p.
65
.10.3390/en13010065
24.
Wang
,
B.
,
Zhang
,
H.
,
Deng
,
F.
,
Wang
,
C.
, and
Si
,
Q.
,
2020
, “
Effect of Short Blade Circumferential Position Arrangement on Gas-Liquid Two-Phase Flow Performance of Centrifugal Pump
,”
Processes
,
8
(
10
), p.
1317
.10.3390/pr8101317
25.
Zhou
,
L.
,
Han
,
Y.
,
Lv
,
W.
,
Yang
,
Y.
,
Zhu
,
Y.
, and
Song
,
X.
,
2020
, “
Numerical Calculation of Energy Performance and Transient Characteristics of Centrifugal Pump Under Gas-Liquid Two-Phase Condition
,”
Micromachines
,
11
(
8
), p.
728
.10.3390/mi11080728
26.
Hundshagen
,
M.
,
Mansour
,
M.
,
Thévenin
,
D.
, and
Skoda
,
R.
,
2019
, “
Numerical Investigation of Two-Phase Air-Water Flow in a Centrifugal Pump With Closed or Semi-Open Impeller
,”
Proceedings of 13th European Turbomachinery Conference on Turbomachinery Fluid Dynamics and Thermodynamics
, Lausanne, Switzerland, Apr. 8–12, Paper No. ETC2019-011.10.29008/ETC2019-011
27.
Hundshagen
,
M.
,
Mansour
,
M.
,
Thévenin
,
D.
, and
Skoda
,
R.
,
2019
, “
Experimental Investigation and 3D-CFD Simulation of Centrifugal Pumps for Gasladen Liquids With Closed and Semi-Open Impellers
,”
Proceedings of Fourth International Rotating Equipment Conference
, Wiesbaden, Germany, Sept. 24–25, Paper No. 044.https://www.researchgate.net/publication/337908020_Experimental_investigation_and_3DCFD_simulation_of_centrifugal_pumps_for_gas-laden_liquids_with_closed_and_semi-open_impellers
28.
Hundshagen
,
M.
,
Mansour
,
M.
,
Thévenin
,
D.
, and
Skoda
,
R.
,
2021
, “
3D Simulation of Gas-Laden Liquid Flows in Centrifugal Pumps and the Assessment of Two-Fluid CFD Methods
,”
Exp. Comput. Multiphase Flow
,
3
, pp.
186
207
.10.1007/s42757-020-0080-4
29.
Stel
,
H.
,
Ofuchi
,
E. M.
,
Chiva
,
S.
, and
Morales
,
R. E.
,
2020
, “
Numerical Simulation of Gas-Liquid Flows in a Centrifugal Rotor
,”
Chem. Eng. Sci.
,
221
, p.
115692
.10.1016/j.ces.2020.115692
30.
Stel
,
H.
,
Ofuchi
,
E. M.
,
Chiva
,
S.
, and
Morales
,
R. E. M.
,
2021
, “
Numerical Assessment of Performance Characteristics and Two-Phase Flow Dynamics of a Centrifugal Rotor Operating Under Gas Entrainment Condition
,”
Exp. Comput. Multiphase Flow, epub
.10.1007/s42757-020-0089-8
31.
He
,
D.
,
Ge
,
Z.
,
Bai
,
B.
,
Guo
,
P.
, and
Luo
,
X.
,
2020
, “
Gas–Liquid Two-Phase Performance of Centrifugal Pump Under Bubble Inflow Based on Computational Fluid Dynamics–Population Balance Model Coupling Model
,”
ASME J. Fluids Eng.
,
142
(
8
), p.
081402
.10.1115/1.4047064
32.
Yan
,
S.
,
Sun
,
S.
,
Luo
,
X.
,
Chen
,
S.
,
Li
,
C.
, and
Feng
,
J.
,
2020
, “
Numerical Investigation on Bubble Distribution of a Multistage Centrifugal Pump Based on a Population Balance Model
,”
Energies
,
13
(
4
), p.
908
.10.3390/en13040908
33.
Zhang
,
F.
,
Zhu
,
L.
,
Chen
,
K.
,
Yan
,
W.
,
Appiah
,
D.
, and
Hu
,
B.
,
2020
, “
Numerical Simulation of Gas–Liquid Two-Phase Flow Characteristics of Centrifugal Pump Based on the CFD–PBM
,”
Mathematics
,
8
(
5
), p.
769
.10.3390/math8050769
34.
Kopparthy
,
S.
,
Mansour
,
M.
,
Janiga
,
G.
, and
Thévenin
,
D.
,
2020
, “
Numerical Investigations of Turbulent Single-Phase and Two-Phase Flows in a Diffuser
,”
Int. J. Multiphase Flow
,
130
, p.
103333
.10.1016/j.ijmultiphaseflow.2020.103333
35.
C˘erne
,
G.
,
Petelin
,
S.
, and
Tiselj
,
I.
,
2001
, “
Coupling of the Interface Tracking and the Two-Fluid Models for the Simulation of Incompressible Two-Phase Flow
,”
J. Comput. Phys.
,
171
(
2
), pp.
776
804
.10.1006/jcph.2001.6810
36.
Hänsch
,
S.
,
Lucas
,
D.
,
Krepper
,
E.
, and
Höhne
,
T.
,
2012
, “
A Multi-Field Two-Fluid Concept for Transitions Between Different Scales of Interfacial Structures
,”
Int. J. Multiphase Flow
,
47
, pp.
171
182
.10.1016/j.ijmultiphaseflow.2012.07.007
37.
Hänsch
,
S.
,
Lucas
,
D.
,
Höhne
,
T.
, and
Krepper
,
E.
,
2014
, “
Application of a New Concept for Multi-Scale Interfacial Structures to the Dam-Break Case With an Obstacle
,”
Nucl. Eng. Des.
,
279
, pp.
171
181
.10.1016/j.nucengdes.2014.02.006
38.
Meller
,
R.
,
Schlegel
,
F.
, and
Lucas
,
D.
,
2021
, “
Basic Verification of a Numerical Framework Applied to a Morphology Adaptive Multifield Two-Fluid Model Considering Bubble Motions
,”
Int. J. Numer. Methods Fluids
,
93
(
3
), pp.
748
773
.10.1002/fld.4907
39.
Coste
,
P.
,
Laviéville
,
J.
,
Pouvreau
,
J.
,
Baudry
,
C.
,
Guingo
,
M.
, and
Douce
,
A.
,
2012
, “
Validation of the Large Interface Method of NEPTUNE_CFD 1.0.8 for Pressurized Thermal Shock (PTS) Applications
,”
Nucl. Eng. Des.
,
253
, pp.
296
310
.10.1016/j.nucengdes.2011.08.066
40.
Štrubelj
,
L.
, and
Tiselj
,
I.
,
2011
, “
Two-Fluid Model With Interface Sharpening
,”
Int. J. Numer. Methods Eng.
,
85
(
5
), pp.
575
590
.10.1002/nme.2978
41.
Wardle
,
K. E.
, and
Weller
,
H. G.
,
2013
, “
Hybrid Multiphase CFD Solver for Coupled Dispersed/Segregated Flows in Liquid-Liquid Extraction
,”
Int. J. Chem. Eng.
,
2013
, p.
128936
.10.1155/2013/128936
42.
Shonibare
,
O. Y.
, and
Wardle
,
K. E.
,
2015
, “
Numerical Investigation of Vertical Plunging Jet Using a Hybrid Multifluid–VOF Multiphase CFD Solver
,”
Int. J. Chem. Eng.
,
2015
, p.
925639
.10.1155/2015/925639
43.
Mathur
,
A.
,
Dovizio
,
D.
,
Frederix
,
E.
, and
Komen
,
E.
,
2019
, “
A Hybrid Dispersed-Large Interface Solver for Multi-Scale Two-Phase Flow Modelling
,”
Nucl. Eng. Des.
,
344
, pp.
69
82
.10.1016/j.nucengdes.2019.01.020
44.
Amidu
,
M. A.
,
Addad
,
Y.
, and
Riahi
,
M. K.
,
2020
, “
A Hybrid Multiphase Flow Model for the Prediction of Both Low and High Void Fraction Nucleate Boiling Regimes
,”
Appl. Therm. Eng.
,
178
(
4
), p.
115625
.10.1016/j.applthermaleng.2020.115625
45.
De Santis
,
A.
,
Hanson
,
B. C.
, and
Fairweather
,
M.
,
2021
, “
Hydrodynamics of Annular Centrifugal Contactors: A CFD Analysis Using a Novel Multiphase Flow Modelling Approach
,”
Chem. Eng. Sci.
,
242
, p.
116729
.10.1016/j.ces.2021.116729
46.
Egorov
,
Y.
, and
Menter
,
F.
,
2008
, “
Development and Application of SST-SAS Turbulence Model in the DESIDER Project
,”
Advances in Hybrid RANS-LES Modelling
(Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol.
97
),
S.-H.
Peng
and
W.
Haase
, eds.,
Springer
,
Berlin
, pp.
261
270
.
47.
Hundshagen
,
M.
,
Casimir
,
N.
,
Pesch
,
A.
,
Falsafi
,
S.
, and
Skoda
,
R.
,
2020
, “
Assessment of Scale-Adaptive Turbulence Models for Volute-Type Centrifugal Pumps at Part Load Operation
,”
Int. J. Heat Fluid Flow
,
85
, p.
108621
.10.1016/j.ijheatfluidflow.2020.108621
48.
Gülich
,
J. F.
,
2020
,
Kreiselpumpen
,
Springer
,
Berlin
.
49.
Barrios
,
L.
, and
Prado
,
M. G.
,
2011
, “
Modeling Two Phase Flow Inside an Electrical Submersible Pump Stage
,”
ASME J. Energy Resour. Technol.
,
133
(
4
), p.
042902
.10.1115/1.4004967
50.
Minemura
,
K.
,
Murakami
,
M.
, and
Katagiri
,
H.
,
1985
, “
Characteristics of Centrifugal Pump Handling Air-Water Mixtures and Size of Air Bubbles in Pump Impellers
,”
Bull. JSME
,
28
(
244
), pp.
2310
2318
.10.1299/jsme1958.28.2310
51.
Weller
,
H. G.
,
Tabor
,
G.
,
Jasak
,
H.
, and
Fureby
,
C.
,
1998
, “
A Tensorial Approach to Computational Continuum Mechanics Using Object-Oriented Techniques
,”
Comput. Phys.
,
12
(
6
), p.
620
.10.1063/1.168744
52.
Müller
,
T.
,
Limbach
,
P.
, and
Skoda
,
R.
,
2015
, “
Numerical 3D RANS Simulation of Gas-Liquid Flow in a Centrifugal Pump With an Euler-Euler Two-Phase Model and a Dispersed Phase Distribution
,” Proceedings of 11th European Conference on Turbomachinery Fluid Dynamics & Thermodynamics, Madrid, Spain, Mar. 23–27, Paper No.
ETC2015-076
.https://www.researchgate.net/publication/280879977_Numerical_3D_RANS_simulation_of_gasliquid_flow_in_a_centrifugal_pump_with_an_Euler-Euler_twophase_model_and_a_dispersed_phase_distribution
53.
Brackbill
,
J.
,
Kothe
,
D.
, and
Zemach
,
C.
,
1992
, “
A Continuum Method for Modeling Surface Tension
,”
J. Comput. Phys.
,
100
(
2
), pp.
335
354
.10.1016/0021-9991(92)90240-Y
54.
Schiller
,
L.
, and
Naumann
,
A.
,
1933
, “
Über die Grundlegenden Berechnungen bei Schwerkraftaufbereitung
,”
Z. Ver. Dtsch. Ing.
,
77
(
12
), pp.
318
321
.
55.
Rzehak
,
R.
,
Krepper
,
E.
,
Liao
,
Y.
,
Ziegenhein
,
T.
,
Kriebitzsch
,
S.
, and
Lucas
,
D.
,
2015
, “
Baseline Model for the Simulation of Bubbly Flows
,”
Chem. Eng. Technol.
,
38
(
11
), pp.
1972
1978
.10.1002/ceat.201500118
56.
Ansys®
,
2017
,
ANSYS® CFX-Solver Theory Guide, Release 18.0
, ANSYS
, Inc., Canonsburg, PA.
57.
Marschall
,
H.
,
2011
, “
Towards the Numerical Simulation of Multi-Scale Two-Phase Flows
,” Ph.D. thesis,
Technische Universität München
, München, Germany.
58.
Rave
,
K.
,
Lehmenkühler
,
M.
,
Wirz
,
D.
,
Bart
,
H.-J.
, and
Skoda
,
R.
,
2021
, “
3D Flow Simulation of a Baffled Stirred Tank for an Assessment of Geometry Simplifications and a Scale-Adaptive Turbulence Model
,”
Chem. Eng. Sci.
,
231
(
5
), p.
116262
.10.1016/j.ces.2020.116262
59.
Menter
,
F.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.10.2514/3.12149
60.
Egorov
,
Y.
,
Boucker
,
M.
,
Martin
,
A.
,
Pigny
,
S.
,
Scheuerer
,
M.
, and
Willemsen
,
S.
,
2004
, “
Validation of CFD Codes With PTS-Relevant Test Cases
,”
Fifth Euratom Framework Programme ECORA Project
.https://cordis.europa.eu/programme/id/EAEC_FWP_EAEC-FWP-EAEC-2C
61.
Frederix
,
E.
,
Mathur
,
A.
,
Dovizio
,
D.
,
Geurts
,
B. J.
, and
Komen
,
E.
,
2018
, “
Reynolds-Averaged Modeling of Turbulence Damping Near a Large-Scale Interface in Two-Phase Flow
,”
Nucl. Eng. Des.
,
333
, pp.
122
130
.10.1016/j.nucengdes.2018.04.010
62.
Tekavčič
,
M.
,
Meller
,
R.
, and
Schlegel
,
F.
,
2021
, “
Validation of a Morphology Adaptive Multi-Field Two-Fluid Model Considering Counter-Current Stratified Flow With Interfacial Turbulence Damping
,”
Nucl. Eng. Des.
,
379
, p.
111223
.10.1016/j.nucengdes.2021.111223
63.
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
64.
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.
081203
.10.1115/1.4046622
65.
Jasak
,
H.
,
1996
, “
Error Analysis and Estimation for the Finite Volume Method With Applications to Fluid Flows
,” Ph.D. thesis,
Imperial College of Science, Technology and Medicine
,
London
.
66.
Weller
,
H. G.
,
2006
,
Bounded Explicit and Implicit Second-Order Schemes for Scalar Transport
,
OpenCFD Ltd
, Bracknell, UK.
67.
Deshpande
,
S. S.
,
Anumolu
,
L.
, and
Trujillo
,
M. F.
,
2012
, “
Evaluating the Performance of the Two-Phase Flow Solver interFoam
,”
Comput. Sci. Discovery
,
5
(
1
), p.
014016
.10.1088/1749-4699/5/1/014016
68.
Weller
,
H.
,
2012
, “
Controlling the Computational Modes of the Arbitrarily Structured C Grid
,”
Mon. Weather Rev.
,
140
(
10
), pp.
3220
3234
.10.1175/MWR-D-11-00221.1
69.
Martínez
,
J.
,
Piscaglia
,
F.
,
Montorfano
,
A.
,
Onorati
,
A.
, and
Aithal
,
S. M.
,
2015
, “
Influence of Spatial Discretization Schemes on Accuracy of Explicit LES: Canonical Problems to Engine-Like Geometries
,”
Comput. Fluids
,
117
(
8
), pp.
62
78
.10.1016/j.compfluid.2015.05.007
70.
Cao
,
Y.
, and
Tamura
,
T.
,
2016
, “
Large-Eddy Simulations of Flow Past a Square Cylinder Using Structured and Unstructured Grids
,”
Comput. Fluids
,
137
(
2
), pp.
36
54
.10.1016/j.compfluid.2016.07.013
71.
Strelets
,
M.
,
2001
, “
Detached Eddy Simulation of Massively Separated Flows
,”
AIAA
Paper No. 2001-0879.10.2514/6.2001-0879
72.
Travin
,
A.
,
Shur
,
M.
,
Strelets
,
M.
, and
Spalart
,
P. R.
,
2002
, “
Physical and Numerical Upgrades in the Detached-Eddy Simulation of Complex Turbulent Flows
,”
Advances in LES of Complex Flows
(Fluid Mechanics and Its Applications, Vol. 65),
R.
Moreau
,
R.
Friedrich
, and
W.
Rodi
, eds.,
Springer
,
Dordrecht, The Netherlands
, pp.
239
254
.
73.
Warming
,
R. F.
, and
Beam
,
R. M.
,
1976
, “
Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows
,”
AIAA J.
,
14
(
9
), pp.
1241
1249
.10.2514/3.61457
74.
Sweby
,
P. K.
,
1984
, “
High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
,”
SIAM J. Numer. Anal.
,
21
(
5
), pp.
995
1011
.10.1137/0721062
75.
Sauer
,
J.
,
2000
, “
Instationär kavitierende Strömungen: Ein neues Modell, basierend auf front capturing (VoF) und Blasendynamik
,” Ph.D. thesis,
Universität Karlsruhe
, Karlsruhe, Germany.
76.
Farrell
,
P. E.
, and
Maddison
,
J. R.
,
2011
, “
Conservative Interpolation Between Volume Meshes by Local Galerkin Projection
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
1–4
), pp.
89
100
.10.1016/j.cma.2010.07.015
77.
Moffat
,
R. J.
,
1988
, “
Describing the Uncertainties in Experimental Results
,”
Exp. Therm. Fluid Sci.
,
1
(
1
), pp.
3
17
.10.1016/0894-1777(88)90043-X
78.
Hirt
,
C.
,
Amsden
,
A.
, and
Cook
,
J.
,
1974
, “
An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds
,”
J. Comput. Phys.
,
14
(
3
), pp.
227
253
.10.1016/0021-9991(74)90051-5
79.
Demirdžić
,
I.
, and
Perić
,
M.
,
1988
, “
Space Conservation Law in Finite Volume Calculations of Fluid Flow
,”
Int. J. Numer. Methods Fluids
,
8
(
9
), pp.
1037
1050
.10.1002/fld.1650080906
80.
Deimel
,
C.
,
Mottyll
,
S.
,
Skoda
,
R.
,
Kiermeir
,
J.
,
Güntner
,
M.
, and
Schilling
,
R.
,
2014
, “
Numerical 3D Simulation of the Fluid-Actuated Valve Motion in a Positive Displacement Pump With Resolution of the Cavitation-Induced Shock Dynamics
,” Eighth International Conference on Computational Fluid Dynamics (ICCFD8), Chengdu, China, July 14–18, Paper No.
ICCFD8-2014-0433
.10.13140/2.1.3443.2326
You do not currently have access to this content.