Abstract

The accuracy of six turbulent flow modeling techniques in an unsteady solution is evaluated against experimental data for a square prism in cross flow. The selected models, shear stress transport (SST), SST-SAS, Reynolds stress model (RSM), partially averaged Navier–Stokes (PANS)-SST, detached eddy simulation (DES), and large eddy simulations (LES), models are the same as those presented in Part 1 of this study, which focused on flow in a staggered tube bank. For this geometry, the SST model proved to be effective at capturing the averaged Nusselt values per side of the square with relatively low computational costs. The SST model, however, showed poorer fidelity to the local Nusselt number profile compared to the experimental data. The LES approach provided a more accurate representation of the local Nusselt number but the computational cost was significantly higher. The PANS modification to the SST model did provide a noticeable improvement in accuracy at a reasonable cost while the SAS modification did not see the same improvement. These conclusions are generally consistent with those found for the staggered tube bank in Part 1 of this study. This study can be used as a guide for the industrial user to select a turbulence model for a similar problem with a low Reynolds number and significant flow separation.

References

1.
Zukauskas
,
A.
,
Ulinskas
,
R.
, and
Daunoras
,
P.
,
1985
, “
Influence of Surface Roughness on the Heat Transfer and Drag of Tube Banks in Crossflow
,”
Heat Technol.
,
3
(
2
), pp.
1
46
.
2.
Zukauskas
,
A.
, and
Ulinskas
,
R.
,
1988
, Heat Transfer in Tube Banks in Crossflow.
3.
Zhukauskas
,
A. A.
,
Ulinskas
,
R. V.
, and
Martsinauskas
,
K. F.
,
1977
, “
Influence of the Geometry of the Tube Bundle on the Local Heat Transfer Rate in the Critical Region of Streamline Flow
,”
Int. Chem. Eng.
,
17
(
4
), pp.
744
751
.
4.
Zdravistch
,
F.
,
1995
, “
Numerical Laminar and Turbulent Fluid Flow and Heat Transfer Predictions in Tube Banks
,”
Int. J. Numer. Methods Heat Fluid Flow
,
5
(
8
), pp.
717
733
.
5.
Pierson
,
O. L.
,
1937
, “
Experimental Investigation of the Influence of Tube Arrangement on Convection Heat Transfer and Flow Resistance in Cross Flow of Gases Over Tube Banks
,”
Am. Soc. Mech. Eng.Trans.
,
59
(
7
), pp.
563
572
.
6.
Ishigai
,
S.
, and
Nishikawa
,
E.
,
1975
, “
Experimental Study of Structure of gas Flow in Tube Banks With Tube Axes Normal to Flow—2. On the Structure of gas Flow in Single-Column, Single-Row, and Double-Rows Tube Banks
,”
Bull. JSME
,
18
(
119
), pp.
528
535
.
7.
Aiba
,
S.
,
Tsuchida
,
H.
, and
Ota
,
T.
,
1983
, “
Heat Transfer Around a Tube in a Staggered Tube Bank
,”
Heat Transfer - Jpn. Res.
,
12
(
1
), pp.
1
18
.
8.
Wilson
,
B. M.
,
Smith
,
B. L.
, and
Spall
,
R. E.
,
2012
, “
Examples of Unsteady CFD Validation System Response Quantities in a Cylinder Array
,”
Nucl. Eng. Des.
,
243
(
2
), pp.
153
167
.
9.
Paul
,
S. S.
,
Ormiston
,
S. J.
, and
Tachie
,
M. F.
,
2008
, “
Experimental and Numerical Investigation of Turbulent Cross-Flow in a Staggered Tube Bundle
,”
Int. J. Heat Fluid Flow
,
29
(
2
), pp.
387
414
.
10.
Li
,
X.
,
Wu
,
X.
, and
He
,
S.
,
2014
, “
Numerical Investigation of the Turbulent Cross Flow and Heat Transfer in a Wall Bounded Tube Bundle
,”
Int. J. Therm. Sci.
,
75
(
1
), pp.
127
139
.
11.
Konstantinidis
,
E.
,
Balabani
,
S.
, and
Yianneskis
,
M.
,
2002
, “
A Study of Vortex Shedding in a Staggered Tube Array for Steady and Pulsating Cross-Flow
,”
ASME J. Fluids Eng.
,
124
(
3
), pp.
737
746
.
12.
Johnson
,
R. W.
,
2005
,
Validation Studies for Numerical Simulations of Flow Phenomena Expected in the Lower Plenum of a Prismatic VHTR Reference Design
,
Idaho National Laboratory
.
13.
Commission
,
I. E.
,
2004
,
Rotating Electrical Machines
,
IEC
,
Geneva, Switzerland
.
14.
Hettegger
,
M.
,
Reinbacher-Kostinger
,
A.
, and
Biro
,
O.
,
2012
, “
Characterizing the Convective Wall Heat Transfer on Convoluted Shapes in the End-Region of an Induction Machine
,”
Proceedings of the 2012 20th International Conference on Electrical Machines, ICEM 2012
,
Marseille, France
,
Sept. 2–5
, pp.
1219
1226
.
15.
Hettegger
,
M.
,
Streibl
,
B.
,
Biro
,
O.
, and
Neudorfer
,
H.
,
2010
, “
Characterizing the Heat Transfer on the end-Windings of an Electrical Machine for Transient Simulations
,”
Proceedings of the 15th IEEE Mediterranean Electrotechnical Conference, MELECON 2010
,
Valletta, Malta
,
Apr. 25–28
, pp.
581
586
.
16.
Hettegger
,
M.
,
Streibl
,
B.
,
Biro
,
O.
, and
Neudorfer
,
H.
,
2010
, “
Identifying the Heat Transfer Coefficients on the end-Windings of an Electrical Machine by Measurements and Simulations
,”
Proceedings of the 19th International Conference on Electrical Machines, ICEM 2010
,
Rome, Italy
,
Sept. 6–8
.
17.
Hettegger
,
M.
,
Streibl
,
B.
,
Biro
,
O.
, and
Neudorfer
,
H.
Measurements and Simulations of the Convective Heat Transfer Coefficients on the End Windings of an Electrical Machine
,”
Institute of Electrical and Electronics Engineers Inc.
, p.
2299
2308
.
18.
Hettegger
,
M.
,
Streibl
,
B.
,
Biro
,
O.
, and
Neudorfer
,
H.
,
2011
, “
Measurements and simulations of the heat transfer on end windings of an induction machinechine
,”
COMPEL – The Int. J. Comp. Math. Elec. Electro. Eng.
,
30
(
6
), pp.
1727
1736
. doi.org/10.1108/03321641111168057
19.
Luke
,
G. E.
,
1923
, “
The Cooling of Electric Machines
,”
Am. Inst. Electr. Eng. J.
,
42
(
12
), pp.
1278
1288
.
20.
Micallef
,
C.
,
2006
, “
End Winding Cooling in Electric Machines
.”
21.
Schleussinger
,
A.
,
Weickenannt
,
A.
, and
Arndt
,
A.
,
2005
, “
Heat Transfer Measurements on Crossing Banks of Noncircular Bars in Cross Flow
,”
6th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics
,
Matsushima, Miyagi, Japan
,
Apr. 17–21
.
22.
Aminian
,
J.
,
2018
, “
Scale Adaptive Simulation of Vortex Structures Past a Square Cylinder
,”
J. Hydrodyn.
,
30
(
4
), pp.
657
671
.
23.
Song
,
C.-S.
, and
Park
,
S.-O.
,
2009
, “
Numerical Simulation of Flow Past a Square Cylinder Using Partially-Averaged Navier-Stokes Model
,”
J. Wind Eng. Ind. Aerodyn.
,
97
(
1
), pp.
37
47
.
24.
aus der Wiesche
,
S.
,
2007
, “
Large-eddy Simulation Study of an air Flow Past a Heated Square Cylinder
,”
Heat Mass Transfer
,
43
(
6
), pp.
515
525
.
25.
Launder
,
B. E.
, and
Kato
,
M.
,
1993
, “
Modelling Flow-Induced Oscillations in Turbulent Flow Around a Square Cylinder
,”
Proceedings of the Fluids Engineering Conference
,
Washington, DC
,
June 20–24
, pp.
189
199
.
26.
Ranjan
,
P.
, and
Dewan
,
A.
,
2010
, “
Partially Averaged Navier Stokes Simulation of Turbulent Heat Transfer From a Square Cylinder
,”
Int. J. Heat Mass Transfer
,
89
(
2015
), pp.
251
266
.
27.
Jeong
,
E.
,
2010
, “
Partially Averaged Navier–Stokes (PANS) Method for Turbulence Simulations—Flow Past a Square Cylinder
,”
ASME J. Fluid. Eng.
,
132
(
12
), p.
121203
.
28.
Pereira
,
F. S.
,
Vaz
,
G.
, and
Eça
,
L.
,
2019
, “
Evaluation of RANS and SRS Methods for Simulation of the Flow Around a Circular Cylinder in the sub-Critical Regime
,”
Ocean Eng.
,
186
, p.
106067
.
29.
Wallin
,
S.
, and
Johansson
,
A. V.
,
2000
, “
An Explicit Algebraic Reynolds Stress Model for Incompressible and Compressible Turbulent Flows
,”
J. Fluid Mech.
,
403
, pp.
89
132
.
30.
ANSYS, Inc
,
I.
,
2016
,
“ANSYS FLUENT Theory Guide R17
,”
ANSYS, Inc
,
Canonsburg, PA
.
31.
Lyn
,
D. A.
,
Einav
,
S.
,
Rodi
,
W.
, and
Park
,
J. H.
,
1995
, “
Laser-Doppler Velocimetry Study of Ensemble-Averaged Characteristics of the Turbulent Near Wake of a Square Cylinder
,”
J. Fluid Mech.
,
304
, pp.
285
319
.
32.
33.
Hussain
,
A. F.
,
1983
, “
Coherent Structures—Reality and Myth
,”
Phys. fluids
,
26
(
10
), pp.
2816
2850
.
34.
Igarashi
,
T.
,
1985
, “
Heat Transfer Form a Square Prism to an air Stream
,”
Int. J. Heat Mass Transfer
,
28
(
1
), pp.
175
181
.
35.
Igarashi
,
T.
,
1986
, “
Local Heat Transfer From a Square Prism to an Airstream
,”
Int. J. Heat Mass Transfer
,
29
(
5
), pp.
777
784
.
36.
Igarashi
,
T.
, and
Mayumi
,
Y.
,
2001
, “
Fluid Flow and Heat Transfer Around a Rectangular Cylinder With Small Inclined Angle (the Case of a Width/Height Ratio of a Section of 5)
,”
Int. J. Heat Fluid Flow
,
22
(
3
), pp.
279
286
.
37.
Mancuso
,
T.
,
2020
, “
Assessment and Improvement of Computational Fluid Dynamics Methods for Separated Turbulent Flows at Low Reynolds Numbers
.”
38.
Vickery
,
B.
,
1966
, “
Fluctuating Lift and Drag on a Long Cylinder of Square Cross-Section in a Smooth and in a Turbulent Stream
,”
J. Fluid Mech.
,
25
(
3
), pp.
481
494
.
39.
Lee
,
B.
,
1975
, “
The Effect of Turbulence on the Surface Pressure Field of a Square Prism
,”
J. Fluid Mech
,
69
(
2
), pp.
263
282
.
40.
Gritskevich
,
M. S.
,
Garbaruk
,
A. V.
,
Schutze
,
J.
, and
Menter
,
F. R.
,
2012
, “
Development of DDES and IDDES Formulations for the k- Shear Stress Transport Model
,”
Flow, Turbul. Combust.
,
88
(
3
), pp.
431
449
.
41.
Nicoud
,
F.
, and
Ducros
,
F.
,
1999
, “
Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor
,”
Flow, Turbul. Combust.
,
62
(
3
), pp.
183
200
.
You do not currently have access to this content.