Abstract

The applicability of several Reynolds averaged Navier–Stokes (RANS) turbulence models in calculating the transient evolution of a buoyancy-induced flow reversal along a vertical heated plate is analyzed through the use of validation quality experimental data from the Rotatable Buoyancy Tunnel (RoBuT) facility. This benchmark attempts to capture the transient evolution from downward forced convection to upward natural convection by removing power to the blower and allowing the buoyancy force emanating from the heated plate to gradually dominate as the primary driving force. Boundary conditions and system response quantities for the numerical model are supplied from the experiment every 0.2 s during the 18.2 s transient. ASME standards are used to quantify the numerical uncertainties while the input uncertainties are handled using a Latin hypercube sampling (LHS) method based on the steady-state conditions (t=0 s)⁠. Qualitative comparisons between numerical and experimental results at several downstream locations are supported using a validation metric based on the statistical disparity between the respective empirical and cumulative distribution functions (CDFs). The results from this study show that the standard linear eddy-viscosity models have difficulty in reproducing the complex features of the flow reversal in comparison with the more intricate turbulence models such as Reynolds stress models (RSM) and low-Reynolds number variants. This study also briefly highlights the difficulties of capturing validation quality data for three-dimensional multiphysics flow, while also providing insight for the design of future experimental efforts.

Issue Section:
Research Papers
Keywords:
buoyancy-driven convection, computational fluid dynamics (CFD), Reynolds-average Navier–Stokes (RANS), Rotatable Buoyancy Tunnel (RoBuT), turbulence modeling, flow reversal
Topics:
Flow (Dynamics), Kinetic energy, Reynolds-averaged Navier–Stokes equations, Transients (Dynamics), Turbulence, Natural convection, Buoyancy, Uncertainty, Boundary-value problems, Stress

References

1.
Hanjalić
,
K.
,
2002
, “
One-Point Closure Models for Buoyancy-Driven Turbulent Flows
,”
Annu. Rev. Fluid Mech.
,
34
(
1
), pp.
321
–
347
.10.1146/annurev.fluid.34.082801.161035
2.
Hanjalić
,
K.
, and
Launder
,
B.
,
2011
,
Modelling Turbulence in Engineering and the Environment: Second-Moment Routes to Closure
,
Cambridge University Press
, New York. 
3.
Kenjereš
,
S.
,
Gunarjo
,
S.
, and
Hanjalić
,
K.
,
2005
, “
Contribution to Elliptic Relaxation Modelling of Turbulent Natural and Mixed Convection
,”
Int. J. Heat Fluid Flow
,
26
(
4
), pp.
569
–
586
.10.1016/j.ijheatfluidflow.2005.03.007
4.
Craft
,
T.
,
Launder
,
B.
, and
Suga
,
K.
,
1996
, “
Development and Application of a Cubic Eddy-Viscosity Model of Turbulence
,”
Int. J. Heat Fluid Flow
,
17
(
2
), pp.
108
–
115
.10.1016/0142-727X(95)00079-6
5.
Xu
,
W.
,
Chen
,
Q.
, and
Nieuwstadt
,
F.
,
1998
, “
A New Turbulence Model for Near-Wall Natural Convection
,”
Int. J. Heat Mass Transfer
,
41
(
21
), pp.
3161
–
3176
.10.1016/S0017-9310(98)00081-7
6.
You
,
J.
,
Yoo
,
J. Y.
, and
Choi
,
H.
,
2003
, “
Direct Numerical Simulation of Heated Vertical Air Flows in Fully Developed Turbulent Mixed Convection
,”
Int. J. Heat Mass Transfer
,
46
(
9
), pp.
1613
–
1627
.10.1016/S0017-9310(02)00442-8
7.
Kim
,
W.
,
He
,
S.
, and
Jackson
,
J. D
,
2008
, “
Assessment by Comparison With DNS Data of Turbulence Models Used in Simulations of Mixed Convection
,”
Int. J. Heat Mass Transfer
,
51
(
5–6
), pp.
1293
–
1312
. 10.1016/j.ijheatmasstransfer.2007.12.002
8.
Keshmiri
,
A.
,
Revell
,
A.
, and
Darabkhani
,
H. G.
,
2016
, “
Assessment of a Common Nonlinear Eddy-Viscosity Turbulence Model in Capturing Laminarization in Mixed Convection Flows
,”
Numer. Heat Transfer, Part A
,
69
(
2
), pp.
146
–
165
.10.1080/10407782.2015.1069672
9.
Keshmiri
,
A.
,
Uribe
,
J.
, and
Shokri
,
N.
,
2015
, “
Benchmarking of Three Different CFD Codes in Simulating Natural, Forced, and Mixed Convection Flows
,”
Numer. Heat Transfer, Part A
,
67
(
12
), pp.
1324
–
1351
.10.1080/10407782.2014.965115
10.
Tung
,
Y.-H.
,
Ferng
,
Y.-M.
,
Johnson
,
R. W.
, and
Chieng
,
C.-C.
,
2013
, “
Study of Natural Circulation in a VHTR After a LOFA Using Different Turbulence Models
,”
Nucl. Eng. Des.
,
263
, pp.
206
–
217
.10.1016/j.nucengdes.2013.04.009
11.
Smith
,
B.
,
2008
, “
Assessment of Computational Fluid Dynamics (CFD) for Nuclear Reactor Safety Problems
,” Organisation for Economic Co-Operation and Development, Paris, France. 
12.
Jones
,
K. L.
, and
Smith
,
B. L.
,
2017
, “
Benchmark Experiments for Steady-State Natural Convection in Fuel Rod Bundles
,”
ASME J. Verif., Validation Uncertainty Quantif.
,
2
(
2
), p.
021001
.10.1115/1.4036496
13.
Harris
,
J. R.
,
Lance
,
B. W.
, and
Smith
,
B. L.
,
2016
, “
Experimental Validation Data for Computational Fluid Dynamics of Forced Convection on a Vertical Flat Plate
,”
ASME J. Fluids Eng.
,
138
(
1
), p.
011401
.10.1115/1.4031007
14.
Lance
,
B. W.
,
Harris
,
J. R.
, and
Smith
,
B. L.
,
2016
, “
Experimental Validation Benchmark Data for Computational Fluid Dynamics of Mixed Convection on a Vertical Flat Plate
,”
ASME J. Verif., Validation Uncertainty Quantif.
,
1
(
2
), p.
021005
.10.1115/1.4032499
15.
Lance
,
B. W.
, and
Smith
,
B. L.
,
2016
, “
Experimental Validation Benchmark Data for Computational Fluid Dynamics of Transient Convection From Forced to Natural With Flow Reversal on a Vertical Flat Plate
,”
ASME J. Verif., Validation Uncertainty Quantif.
,
1
(
3
), p.
031005
.10.1115/1.4033963
16.
American Society of Mechanical Engineers
,
2009
,
Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer: An American National Standard
,
American Society of Mechanical Engineers
, New York.
17.
Oberkampf
,
W. L.
, and
Roy
,
C. J.
,
2010
,
Verification and Validation in Scientific Computing
,
Cambridge University Press
, New York.
18.
Coleman
,
H. W.
, and
Steele
,
W. G.
,
2018
,
Experimentation, Validation, and Uncertainty Analysis for Engineers
,
Wiley
, Hoboken, NJ.
19.
Timmins
,
B. H.
,
Wilson
,
B. W.
,
Smith
,
B. L.
, and
Vlachos
,
P. P.
,
2012
, “
A Method for Automatic Estimation of Instantaneous Local Uncertainty in Particle Image Velocimetry Measurements
,”
Exp. Fluids
,
53
(
4
), pp.
1133
–
1147
.10.1007/s00348-012-1341-1
20.
Wilson
,
B. M.
, and
Smith
,
B. L.
,
2013
, “
Taylor-Series and Monte Carlo-Method Uncertainty Estimation of the Width of a Probability Distribution Based on Varying Bias and Random Error
,”
Meas. Sci. Technol.
,
24
(
3
), p.
035301
.10.1088/0957-0233/24/3/035301
21.
Clifford
,
C. E.
, and
Kimber
,
M. L.
,
2020
, “
Assessment of RANS-Based Turbulence Models for Buoyancy-Influenced Forced Convection on a Heated Vertical Surface
,”
ASME J. Verif., Validation Uncertainty Quantif.
,
5
(
1
), p.
011005
.10.1115/1.4046715
22.
Lance
,
B. W.
, and
Smith
,
B. L.
,
2015
, “
Transient Convection From Forced to Natural With Flow Reversal on a Vertical Flat Plate
,”
NURETH-16
, Chicago, IL, Aug. 30–Sept. 4, pp. 1261–1274. 
23.
ANSYS, Inc.
,
2015
, “
CFD, ICEM CFD Theory Guide
,” ANSYS, Cannonsburg, PA.
24.
Siemens
,
2018
, “
Simcenter STAR-CCM+ User Guide V13. 04
,” Siemens PLM, Plano, TX.
25.
Shih
,
T.-H.
,
Liou
,
W. W.
,
Shabbir
,
A.
,
Yang
,
Z.
, and
Zhu
,
J.
,
1995
, “
A New k-Epsilon Eddy Viscosity Model for High Reynolds Number Turbulent Flows
,”
Comput. Fluids
,
24
(
3
), pp.
227
–
238
.10.1016/0045-7930(94)00032-T
26.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
–
1605
.10.2514/3.12149
27.
Johnson
,
D. A.
, and
King
,
L. J. A. J.
,
1985
, “
A Mathematically Simple Turbulence Closure Model for Attached and Separated Turbulent Boundary Layers
,”
AIAA J.
,
23
(
11
), pp.
1684
–
1692
. 10.2514/3.9152
28.
Abe
,
K.
,
Kondoh
,
T.
, and
Nagano
,
Y.
,
1994
, “
A New Turbulence Model for Predicting Fluid Flow and Heat Transfer in Separating and Reattaching Flows—I: Flow Field Calculations
,”
Int. J. Heat Mass Transfer
,
37
(
1
), pp.
139
–
151
.10.1016/0017-9310(94)90168-6
29.
Abe
,
K.
,
Kondoh
,
T.
, and
Nagano
,
Y.
,
1995
, “
A New Turbulence Model for Predicting Fluid Flow and Heat Transfer in Separating and Reattaching Flows—II: Thermal Field Calculations
,”
Int. J. Heat Mass Transfer
,
38
(
8
), pp.
1467
–
1481
.10.1016/0017-9310(94)00252-Q
30.
Davidson
,
L.
,
2003
, “
Modification of the V2F Model for  Computing the Flow in a 3D Wall Jet
,”
Turbul. Heat Mass Transfer
,
4
(
1
), pp.
577
–
584
. http://www.tfd.chalmers.se/~lada/postscript_files/paper-v2f-aalborg-thmt4.pdf
31.
Durbin
,
P. A.
,
1991
, “
Near-Wall Turbulence Closure Modeling Without “Damping Functions
,”
Theor. Comput. Fluid Dyn.
,
3
(
1
), pp.
1
–
13
.10.1007/BF00271513
32.
Lien
,
F.
,
Kalitzin
,
G.
, and
Durbin
,
P.
,
1998
, “
RANS Modeling for Compressible and Transitional Flows
,”
Proceedings of the Stanford University Center for Turbulence Research Summer Program
, Summer, 1998, Stanford University, Stanford, CA, pp.
267
–
286
. 
33.
Manceau
,
R.
, and
Hanjalić
,
K.
,
2002
, “
Elliptic Blending Model: A New Near-Wall Reynolds-Stress Turbulence Closure
,”
Phys. Fluids
,
14
(
2
), pp.
744
–
754
.10.1063/1.1432693
34.
E.
Lemmon
,
M.
McLinden
, and
D.
Friend
,
P.
Lindstrom
, and
W.
Mallard
, eds.,
2019
,
Thermophysical Properties of Fluid Systems
(NIST Chemistry WebBook),
National Institute of Standards and Technology
,
Gaithersburg, MD
.
35.
Johnson
,
R. W.
,
2008
, “
Modeling Strategies for Unsteady Turbulent Flows in the Lower Plenum of the VHTR
,”
Nucl. Eng. Des.
,
238
(
3
), pp.
482
–
491
.10.1016/j.nucengdes.2007.02.049
36.
Roache
,
P. J.
,
1993
, “
A Method for Uniform Reporting of Grid Refinement Studies
,”
ASME J. Fluids Eng.,
116
(
3
), pp. 405–413. 
37.
Eça
,
L.
,
2002
, “
An Evaluation of Verification Procedures for CFD Applications
,”
24th Symposium on Naval Hydrodynamics
, Fukuoka, Japan, July 8–13, pp.
568
–
587
. 
38.
Eça
,
L.
,
Hoekstra
,
M.
, and
Roache
,
P.
,
2005
, “
Verification of Calculations: An Overview of the Lisbon Workshop
,”
AIAA
Paper No. 2005-4728. 10.2514/6.2005-4728
39.
Cadafalch
,
J.
,
PéRez-Segarra
,
C. D.
,
CòNsul
,
R.
, and
Oliva
,
A.
,
2002
, “
Verification of Finite Volume Computations on Steady-State Fluid Flow and Heat Transfer
,”
ASME J. Fluids Eng.
,
124
(
1
), pp.
11
–
21
.10.1115/1.1436092
40.
Xing
,
T.
, and
Stern
,
F.
,
2010
, “
Factors of Safety for Richardson Extrapolation
,”
ASME J. Fluids Eng.
,
132
(
6
), p.
061403
.10.1115/1.4001771
41.
Celik
,
I. B.
,
Ghia
,
U.
,
Roache
,
P. J.
, and
Freitas
,
C. J.
,
2008
, “
Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications
,”
ASME J. Fluids Eng.
,
130
(
7
), p.
078001
.10.1115/1.2960953
42.
Eça
,
L.
,
Vaz
,
G.
,
Toxopeus
,
S.
, and
Hoekstra
,
M.
,
2019
, “
Numerical Errors in Unsteady Flow Simulations
,”
ASME J. Verif., Validation Uncertainty Quantif.
,
4
(
2
), p.
021001
.10.1115/1.4043975
43.
Knupp
,
P.
, and
Salari
,
K.
,
2003
,
Verification of Computer Codes in Computational Science and Engineering
,
CRC Press
, Boca Raton, FL.
44.
KammRider
,
J. W.
, and
Brock
,
J.
,
2003
, “
Combined Space and Time Convergence Analysis of a Compressible Flow Algorithm
,”
16th AIAA Computational Fluid Dynamics Conference
, June 23–26, Orlando, FL, p.
4241
.
45.
Ferson
,
S.
,
Oberkampf
,
W. L.
, and
Ginzburg
,
L.
,
2008
, “
Model Validation and Predictive Capability for the Thermal Challenge Problem
,”
Comput. Methods Appl. Mech. Eng.
,
197
(
29–32
), pp.
2408
–
2430
.10.1016/j.cma.2007.07.030
46.
Elsinga
,
G. E.
,
Scarano
,
F.
,
Wieneke
,
B.
, and
van Oudheusden
,
B. W.
,
2006
, “
Tomographic Particle Image Velocimetry
,”
ASME Exp. Fluids
,
41
(
6
), pp.
933
–
947
.10.1007/s00348-006-0212-z
Copyright © 2020 by ASME
You do not currently have access to this content.