Numerical Study Of Turbulent Diesel Flow In A Pipe With Sudden Expansion
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Publicado: 13 de junio de 2012
Applied Mathematical Modelling 25 (2001) 319±333
www.elsevier.nl/locate/apm
Numerical study of turbulent diesel ¯ow in a pipe with sudden expansion
E.D. Koronaki a, H.H. Liakos a, M.A. Founti b, N.C. Markatos
a
a,*
Department of Chemical Engineering, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece b Mechanical Engineering Department, Zografou Campus,15780 Athens, Greece Received 23 September 1999; received in revised form 22 May 2000; accepted 29 August 2000
Abstract Three two-equation models and a second-moment closure are implemented in the case of turbulent diesel ¯ow in a pipe with sudden expansion. The chosen two-equation closures are: the standard k±e, the RNG k±e and the two-scale k±e models. The performance of the models isinvestigated with regard to the non-equilibrium parameter g and the mean strain of the ¯ow, S. Velocity and turbulence kinetic energy predictions of the dierent models are compared among themselves and with experimental data and are interpreted on the basis of the aforementioned quantities. The eect of more accurate near-wall modeling to the two-equation models is also investigated. The results of thestudy demonstrate the superiority of the second-moment closure in predicting the ¯ow characteristics over the entire domain. From the two-equation models the RNG derived k±e model also gave very good predictions, especially when nonequilibrium wall-functions were implemented. As far as g and S are concerned, only the closures with greater physical consistency, such as the two-scale k±e model, givesatisfactory results. Ó 2001 Elsevier Science Inc. All rights reserved. Keywords: Sudden expansion; Turbulence; Second-moment closure; Non-equilibrium parameters
1. Introduction This paper is about exploring the possibilities that dierent turbulence closures oer, for more in-depth analysis of a complex ¯ow. The case under investigation is steady, axisymmetric, turbulent ¯ow of diesel in apipe with sudden expansion. This is a typical geometry where generation of turbulence energy takes place, due to sudden change of boundary conditions. The liquid forms a recirculation region right after the point of the sudden expansion and the ¯ow is in a state of strong non-equilibrium. This study is aimed at investigating the capability of four dierent turbulence-closure models, to calculate themean strain of the ¯ow, S and the non-equilibrium parameter g kSae and to investigate their eect on predicting the velocity ®eld, the turbulence kinetic energy and the recirculation length. Those non-equilibrium parameters are the basic criteria for turbulence ¯ow characterization and have been, until now, poorly investigated. For each case the results are compared with experimental data.
*Corresponding author. Tel.: +30-1-772-3227; fax: +30-1-772-3228. E-mail address: n.markatos@ntua.gr (N.C. Markatos).
0307-904X/01/$ - see front matter Ó 2001 Elsevier Science Inc. All rights reserved. PII: S 0 3 0 7 - 9 0 4 X ( 0 0 ) 0 0 0 5 5 - X
320
E.D. Koronaki et al. / Appl. Math. Modelling 25 (2001) 319±333
The geometry of the pipe with sudden expansion has been used frequentlyby several authors for testing and evaluating turbulence models. The reason for this is that it combines a region of strong non-equilibrium, the recirculation region, followed by a region where the ¯ow returns to equilibrium. The sudden expansion geometry has also been the subject of much experimental study, because it can oer helpful insight and enhance our understanding of turbulence and alsodue to its application in ¯ows of industrial interest that include turbulence-related phenomena such as corrosion [1]. Among those who have studied experimentally separating and reattaching ¯ows are Back and Roshke [2], Khezzar et al. [3], Driver and Seegmiller [4], Stieglmeier et al. [5] and Founti and Klipfel [6]. Among those who have investigated the phenomenon numerically is Sindir [7], who...
www.elsevier.nl/locate/apm
Numerical study of turbulent diesel ¯ow in a pipe with sudden expansion
E.D. Koronaki a, H.H. Liakos a, M.A. Founti b, N.C. Markatos
a
a,*
Department of Chemical Engineering, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece b Mechanical Engineering Department, Zografou Campus,15780 Athens, Greece Received 23 September 1999; received in revised form 22 May 2000; accepted 29 August 2000
Abstract Three two-equation models and a second-moment closure are implemented in the case of turbulent diesel ¯ow in a pipe with sudden expansion. The chosen two-equation closures are: the standard k±e, the RNG k±e and the two-scale k±e models. The performance of the models isinvestigated with regard to the non-equilibrium parameter g and the mean strain of the ¯ow, S. Velocity and turbulence kinetic energy predictions of the dierent models are compared among themselves and with experimental data and are interpreted on the basis of the aforementioned quantities. The eect of more accurate near-wall modeling to the two-equation models is also investigated. The results of thestudy demonstrate the superiority of the second-moment closure in predicting the ¯ow characteristics over the entire domain. From the two-equation models the RNG derived k±e model also gave very good predictions, especially when nonequilibrium wall-functions were implemented. As far as g and S are concerned, only the closures with greater physical consistency, such as the two-scale k±e model, givesatisfactory results. Ó 2001 Elsevier Science Inc. All rights reserved. Keywords: Sudden expansion; Turbulence; Second-moment closure; Non-equilibrium parameters
1. Introduction This paper is about exploring the possibilities that dierent turbulence closures oer, for more in-depth analysis of a complex ¯ow. The case under investigation is steady, axisymmetric, turbulent ¯ow of diesel in apipe with sudden expansion. This is a typical geometry where generation of turbulence energy takes place, due to sudden change of boundary conditions. The liquid forms a recirculation region right after the point of the sudden expansion and the ¯ow is in a state of strong non-equilibrium. This study is aimed at investigating the capability of four dierent turbulence-closure models, to calculate themean strain of the ¯ow, S and the non-equilibrium parameter g kSae and to investigate their eect on predicting the velocity ®eld, the turbulence kinetic energy and the recirculation length. Those non-equilibrium parameters are the basic criteria for turbulence ¯ow characterization and have been, until now, poorly investigated. For each case the results are compared with experimental data.
*Corresponding author. Tel.: +30-1-772-3227; fax: +30-1-772-3228. E-mail address: n.markatos@ntua.gr (N.C. Markatos).
0307-904X/01/$ - see front matter Ó 2001 Elsevier Science Inc. All rights reserved. PII: S 0 3 0 7 - 9 0 4 X ( 0 0 ) 0 0 0 5 5 - X
320
E.D. Koronaki et al. / Appl. Math. Modelling 25 (2001) 319±333
The geometry of the pipe with sudden expansion has been used frequentlyby several authors for testing and evaluating turbulence models. The reason for this is that it combines a region of strong non-equilibrium, the recirculation region, followed by a region where the ¯ow returns to equilibrium. The sudden expansion geometry has also been the subject of much experimental study, because it can oer helpful insight and enhance our understanding of turbulence and alsodue to its application in ¯ows of industrial interest that include turbulence-related phenomena such as corrosion [1]. Among those who have studied experimentally separating and reattaching ¯ows are Back and Roshke [2], Khezzar et al. [3], Driver and Seegmiller [4], Stieglmeier et al. [5] and Founti and Klipfel [6]. Among those who have investigated the phenomenon numerically is Sindir [7], who...
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