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Research Papers: Fundamental Issues and Canonical Flows

Assessment of the Reliability of Two-Equation URANS Models in Predicting a Precessing Flow

[+] Author and Article Information
Xiao Chen, Zhao F. Tian, G. J. Nathan

Center for Energy Technology (CET),
School of Mechanical Engineering,
The University of Adelaide,
Adelaide, SA 5005, Australia

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 31, 2017; final manuscript received January 15, 2019; published online March 4, 2019. Assoc. Editor: Oleg Schilling.

J. Fluids Eng 141(7), 071203 (Mar 04, 2019) (10 pages) Paper No: FE-17-1312; doi: 10.1115/1.4042748 History: Received May 31, 2017; Revised January 15, 2019

A systematic assessment of unsteady Reynolds-averaged Navier–Stokes (URANS) models in predicting the complex flow through a suddenly expanding axisymmetric chamber is reported. Five types of URANS models assessed in the study comprise the standard k–ε model, the modified k–ε (1.6) model, the modified k–ε (1.3) model, the renormalization group (RNG) k–ε model, and the shear stress transport (SST) model. To assess the strengths and limitations of these models in predicting the velocity field of this precessing flow, the numerical results are assessed against available experimental results. Good agreement with the flow features and reasonable agreement with the measured phase-averaged velocity field, energy of total fluctuation and precession frequency can be achieved with both the standard k–ε and the SST models. The degree of accuracy in predicting the rate of both spreading and velocity decay of the jet was found to greatly influence the prediction of the precession motion.

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Figures

Grahic Jump Location
Fig. 1

A schematic diagram of the fluidic precessing jet flow and nozzle

Grahic Jump Location
Fig. 2

The dimensions of the fluidic precessing jet nozzle modeled here, based on the configuration investigated experimentally by Wong et al. [31], where d, D, and De are the diameters of the nozzle's inlet, nozzle chamber and nozzle's exit, respectively, and L is the length of the FPJ nozzle

Grahic Jump Location
Fig. 3

Mesh of the current model: (a) the whole domain, (b) detailed view of the FPJ nozzle, (c) the longitudinal plane through the nozzle, and (d) the cross-sectional plane through the nozzle

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Fig. 11

Contours of the F1 value in the SST model (see Eq. (4)) at the five cross section planes of x/d =1.52, 3.67, 5.32, 7.03, and 8.93, within the FPJ nozzle

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Fig. 10

Measured and calculated time average (a) axial velocity and (b) total fluctuation energy (Ef) profile at x'/De = 0.16. The velocity values are normalized with the inlet velocity ui, Ef are normalized with ui2 and the abscissa is normalized with the diameter of the nozzle's exit De.

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Fig. 9

Measured and predicted results of inverse centerline velocity decay of the phase-averaged jet [31]. The parameter Ujet,cl is the maximum velocity in the local plane and Ui is the bulk inlet velocity. The vertical line indicates the location of the center body's upstream surface.

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Fig. 8

Phase-averaged axial velocity contours in the near external field of the FPJ nozzle, x′/De = 0.16, obtained by: (a) experiment [35] and simulation using (b) the standard kε model and (c) the SST model. Data are normalized by the local centerline velocity in this plane. Refer to Fig. 2 for symbols and coordinates.

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Fig. 7

Cross-sectional images of the phase-averaged axial velocity contours at the transverse plane x/d =8.93 within the FPJ nozzle as obtained with: (a) the experiment [35], (b) the standard kε model, and (c) the SST model and data are normalized by the local centerline velocity in this plane. Refer to Fig. 2 for symbols and coordinates.

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Fig. 6

Axial evolution of the measured and predicted equivalent diameters of the phase-averaged jet [31]. The vertical dotted and dashed lines indicate the location of the center body's upstream surface in the conventional geometry and extended geometry (Lc=240 mm), respectively. Refer to Fig. 2 for symbols and coordinates.

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Fig. 5

Three-dimensional visualizations of the predicted streamline through the FPJ nozzle with the (a) kε model, (b) SST model, (c) RNG kε model, and (d) is the streamline through a longer FPJ nozzle (Lc=240 mm) predicted with RNG kε model

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Fig. 4

Axial evolution of the normalized predicted equivalent diameters of the precessing jet through the domain, as calculated from the average of 5, 10, and 15 cycles of precession. Refer to Fig. 2 for symbols and coordinates. The vertical dashed line indicates the location of the upstream surface of the center body.

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Fig. 12

Predicted frequency spectrum

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Fig. 13

Iso-surface of the 200 m2/s2 instantaneous turbulence kinetic energy (k) predicted with (a) the kε (1.3), (b) the standard kε model, and (c) the kε (1.6) model

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Fig. 14

Axial evolution of the measured and predicted equivalent diameters of the phase-averaged jet [31]. The vertical line indicates the location of the center body's upstream surface. Refer to Fig. 2 for symbols and coordinates.

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Fig. 15

Measured and predicted results of inverse centerline velocity decay of the phase-averaged jet [31]. Refer to Fig. 2 for symbols and coordinates.

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Fig. 16

Three-dimensional visualizations of the predicted instantaneous streamlines through the FPJ nozzle with the (a) kε (1.3), (b) kε, and (c) kε (1.6) models

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