An explicit cell-centered finite volume solver coupled to a turbulence model corrected for structural compressibility fails to satisfactorily predict the behavior of under-expanded supersonic jets exhausting into still air, because the model does not properly account for the turbulence/shock wave interaction. Two approaches are examined: imposing a realizability constraint and taking into account shock unsteadiness effects. Although both corrections yield better agreement with experimental data of under-expanded jets, the realizability constraint yields better results than the shock unsteadiness correction.
Issue Section:
Flows in Complex Systems
1.
Chuech
, S. G.
, Lai
, M. C.
, and Faeth
, G. M.
, 1989, “Structure of Turbulent Sonic Underexpanded Free Jets
,” AIAA J.
0001-1452, 27
(5
), pp. 549
–559
.2.
Dash
, S. M.
, Wolf
, D. E.
, and Seiner
, J. M.
, 1985, “Analysis of Turbulent Underexpanded Jets, Part I: Parabolized Navier-Stokes Model, SCIPVIS
,” AIAA J.
0001-1452, 23
(4
), pp. 505
–514
.3.
Dash
, S. M.
, and Wolf
, D. E.
, 1984, “Interactive Phenomena in Supersonic Jet Mixing Problems, Part II: Numerical Studies
,” AIAA J.
0001-1452, 22
(10
), pp. 1395
–1404
.4.
Dash
, S. M.
, and Wolf
, D. E.
, 1984, “Interactive Phenomena in Supersonic Jet Mixing Problems, Part I: Phenomenology and Numerical Modeling Techniques
,” AIAA J.
0001-1452, 22
(7
), pp. 905
–913
.5.
Cumber
, P. S.
, Fairweather
, M.
, Falle
, S. A. E. G.
, and Giddings
, J. R.
, 1994, “Predictions of the Structure of Turbulent, Moderately Underexpanded Jets
,” ASME J. Fluids Eng.
0098-2202, 116
(4
), pp. 707
–713
.6.
Cumber
, P. S.
, Fairweather
, M.
, Falle
, S.
, and Giddings
, J. R.
, 1995, “Predictions of the Structure of Turbulent, Highly Underexpanded Jets
,” ASME J. Fluids Eng.
0098-2202, 117
(4
), pp. 599
–604
.7.
Fairweather
, M.
, and Ranson
, K. R.
, 2006, “Prediction of Underexpanded Jets Using Compressibility-Corrected, Two-Equation Turbulence Models
,” Prog. Comput. Fluid Dyn.
1468-4349, 6
(1/2/3
), pp. 122
–128
.8.
Sarkar
, S.
, Erlebacher
, G.
, Hussaini
, M. Y.
, and Kreiss
, H. O.
, 1991, “Analysis and Modelling of Dilatational Terms in Compressible Turbulence
,” J. Fluid Mech.
0022-1120, 227
, pp. 473
–493
.9.
Wilcox
, D. C.
, 2004, Turbulence Modeling for CFD
, DCW Industries
, La Canada, CA
.10.
Heinz
, S.
, 2003, “A Model for the Reduction of the Turbulent Energy Redistribution by Compressibility
,” Phys. Fluids
1070-6631, 15
(11
), pp. 3580
–3583
.11.
Tandra
, D.
, 2005, “Development and Application of a Turbulence Model for a Sootblower Jet Propagating Between Recovery Boiler Superheater Platens
,” Ph.D. thesis, Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Canada.12.
Durbin
, P. A.
, 1996, “On the k-3 Stagnation Point Anomaly
,” Int. J. Heat Fluid Flow
0142-727X, 17
(1
), pp. 89
–90
.13.
Sinha
, K.
, Mahesh
, K.
, and Candler
, G. V.
, 2003, “Modeling Shock Unsteadiness in Shock/Turbulence Interaction
,” Phys. Fluids
1070-6631, 15
(8
), pp. 2290
–2297
.14.
Shih
, T.
, Liou
, W. W.
, Shabbir
, A.
, Yang
, Z.
, and Zhu
, J.
, 1995, “New k−ε Viscosity Model for High Reynolds Number Turbulent Flows
,” Comput. Fluids
0045-7930, 24
(3
), pp. 227
–238
.15.
Thivet
, F.
, Knight
, D. D.
, Zheltovodov
, A. A.
, and Maksimov
, A. I.
, 2001, “Insights in Turbulence Modeling for Crossing-Shock-Wave/Boundary-Layer Interactions
,” AIAA J.
0001-1452, 39
(6
), pp. 985
–995
.16.
Sinha
, K.
, Mahesh
, K.
, and Candler
, G. V.
, 2005, “Modeling the Effect of Shock Unsteadiness in Shock/Turbulent Boundary-Layer Interactions
,” AIAA J.
0001-1452, 43
(3
), pp. 586
–594
.17.
Emami
, B.
, 2009, “Numerical Simulation of Kraft Recovery Boiler Sootblower Jets
,” Ph.D. thesis, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada.18.
Sarkar
, S.
, 1995, “The Stabilizing Effect of Compressibility in Turbulent Shear Flow
,” J. Fluid Mech.
0022-1120, 282
, pp. 163
–186
.19.
Tandra
, D. S.
, Kaliazine
, A.
, Cormack
, D. E.
, and Tran
, H. N.
, 2006, “Numerical Simulation of Supersonic Jet Flow Using a Modified Model
,” Int. J. Comput. Fluid Dyn.
1061-8562, 20
(1
), pp. 19
–27
.20.
Alvi
, F. S.
, Ladd
, J. A.
, and Bower
, W. W.
, 2002, “Experimental and Computational Investigation of Supersonic Impinging Jets
,” AIAA J.
0001-1452, 40
(4
), pp. 599
–609
.21.
Debonis
, J. R.
, and Scott
, J. N.
, 2002, “Large-Eddy Simulation of a Turbulent Compressible Round Jet
,” AIAA J.
0001-1452, 40
(7
), pp. 1346
–1354
.22.
Du P. Donaldson
, C.
, and Gray
, K. E.
, 1966, “Theoretical and Experimental Investigation of the Compressible Free Mixing of Two Dissimilar Gases
,” AIAA J.
0001-1452, 4
(11
), pp. 2017
–2025
.23.
Du P. Donaldson
, C.
, and Snedeker
, R. S.
, 1971, “A Study of Free Jet Impingement, Part 1, Mean Properties of Free and Impinging Jets
,” AIAA J.
0001-1452, 45
(2
), pp. 281
–319
.24.
Panda
, J.
, and Seasholtz
, R. G.
, 1999, “Velocity and Temperature Measurement in Supersonic Free Jets Using Spectrally Resolved Rayleigh Scattering
,” AIAA Paper No. 99-0296.25.
Wang
, Z.
, and Andreopoulos
, Y.
, 2003, “Compressibility Effects in Turbulent Subsonic Jets
,” Fourth ASME/JSME Joint Fluids Engineering Conference
.26.
Thivet
, F.
, Knight
, D. D.
, Zheltovodov
, A. A.
, and Maksimov
, A. I.
, 2001, “Importance of Limiting the Turbulent Stresses to Predict 3D Shock Wave/Boundary Layer Interactions
,” 23rd Symposium on Shock Waves
, Paper No. 2761.27.
Thivet
, F.
, 2002, “Lessons Learned From RANS Simulations of Shock-Wave/Boundary Layer Interactions
,” AIAA Paper No. 2002-0583.28.
Zank
, G. P.
, Zhou
, Y.
, Matthaeus
, W. H.
, and Rice
, W. K. M.
, 2002, “The Interaction of Turbulence With Shock Waves: A Basic Model
,” Phys. Fluids
1070-6631, 14
(11
), pp. 3766
–3774
.29.
Mahesh
, K.
, Lele
, S. K.
, and Moin
, P.
, 1997, “The Influence of Entropy Fluctuations on the Interaction of Turbulence With a Shock Wave
,” J. Fluid Mech.
0022-1120, 334
, pp. 353
–379
.30.
Moore
, F. K.
, 1954, “Unsteady Oblique Interaction of a Shock Wave With a Plane Disturbance
,” Technical Report No. NACA TN 2879.31.
Panda
, J.
, 1998, “Shock Oscillation in Underexpanded Screeching Jets
,” J. Fluid Mech.
0022-1120, 363
, pp. 173
–198
.32.
Panda
, J.
, and Seasholtz
, R. G.
, 1999, “Measurement of Shock Structure and Shock Vortex Interaction in Underexpanded Jets Using Rayleigh Scattering
,” Phys. Fluids
1070-6631, 11
(12
), pp. 3761
–3777
.33.
Seiner
, J. M.
, and Norum
, T. D.
, 1979, “Experiments on Shock Associated Noise of Supersonic Jets
,” AIAA Paper No. 79-1526.34.
Seiner
, J. M.
, and Norum
, T. D.
, 1980, “Aerodynamic Aspects of Shock Containing Jet Plumes
,” AIAA Paper No. 80-0965.35.
Norum
, T. D.
, and Seiner
, J. M.
, 1982, “Measurements of Mean Static Pressure and Far-Field Acoustics of Shock-Containing Supersonic Jets
,” NASA
Technical Memorandum 84521.36.
Boersma
, B. J.
, Brethouwer
, G.
, and Nieuwstadt
, F. T. M.
, 1998, “A Numerical Investigation on the Effect of the Inflow Conditions on the Self-Similar Region of a Round Jet
,” Phys. Fluids
1070-6631, 10
(4
), pp. 899
–908
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.
