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Research Papers: Fundamental Issues and Canonical Flows

On Coarse Grids Simulation of Compressible Mixing Layer Flows Using Vorticity Confinement

[+] Author and Article Information
K. Hejranfar

Aerospace Engineering Department,
Sharif University of Technology,
Azadi Ave,
Tehran 11365-11155, Iran
e-mail: khejran@sharif.edu

M. Ebrahimi

Aerospace Research Institute,
Ministry of Science,
Research and Technology,
Shahrak Gharb,
Tehran 18665-834, Iran
e-mail: mebrahimi@ari.ac.ir

M. Sadri

Aerospace Research Institute,
Ministry of Science,
Research and Technology,
Shahrak Gharb,
Tehran 18665-834, Iran
e-mail: sadri@ari.ac.ir

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 8, 2016; final manuscript received September 2, 2017; published online October 19, 2017. Assoc. Editor: Daniel Livescu.

J. Fluids Eng 140(3), 031201 (Oct 19, 2017) (13 pages) Paper No: FE-16-1664; doi: 10.1115/1.4037867 History: Received October 08, 2016; Revised September 02, 2017

In this work, the capability and performance of the vorticity confinement (VC) implemented in a high-order accurate flow solver in predicting two-dimensional (2D) compressible mixing layer flows on coarse grids are investigated. Here, the system of governing equations with incorporation of the VC in the formulation is numerically solved by the fourth-order compact finite difference scheme. To stabilize the numerical solution, a low-pass high-order filter is applied, and the nonreflective boundary conditions are used at the farfield and outflow boundaries to minimize the reflections. At first, the numerical results without applying the VC are validated by available direct numerical simulations (DNSs) for a low Reynolds number mixing layer. Then, the calculations using a range of VC levels are performed for a high Reynolds number mixing layer and the results are thoroughly compared with those of available large eddy simulations (LESs). The study shows that, with applying the vortex identification method, more accurate results are obtained in the slow laminar region of the mixing layer. A sensitivity study is also performed to examine the effect of different numerical parameters to reasonably provide more accurate results. It is shown that the local VC introduced based on the artificial viscosity coefficient and the vorticity thickness can improve the accuracy of the results in the turbulent region of the mixing layer compared with those of LESs. It is found that the solution methodology proposed can reasonably preserve the vortices in the flowfield and the results are comparable with those of LESs on fairly coarser grids and thus the computational costs can be considerably decreased.

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Figures

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Fig. 1

(a) A schematic of computational domain and (b) computational mesh used in the DNS (every 2nd node is shown)

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Fig. 2

Comparison of scaled velocity and error function profiles

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Fig. 3

Comparison of vorticity thickness development of mixing layer

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Fig. 4

Computed flowfield shown by vorticity contours in naturally developing mixing layer obtained by the DNS

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Fig. 5

Comparison of scaled velocity and error function profiles: (a) without VC and (b) with VC

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Fig. 6

Comparison of solution obtained by considering localand constant VC coefficients: (a) vorticity thickness growth and (b) normalized Reynolds normal stress σxx profiles at x=245δω(0)

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Fig. 7

Comparison of vorticity contours by considering (a) local VC coefficient (cvc=6) and (b) constant VC coefficient (εc=1.2)

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Fig. 8

Effect of level of VC and numerical viscosity on vorticity thickness development of mixing layer

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Fig. 9

Effect of level of VC and filtering on vorticity thickness development of mixing layer

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Fig. 10

Effect of applying vortex identification method on vorticity thickness development of mixing layer

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Fig. 11

Comparison of vorticity thickness development of mixing layer for different levels of VC

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Fig. 12

Effect of level of VC on vorticity contours in naturally developing mixing layer: (a) cvc=0, (b)cvc=5, (c) cvc=6, (d) cvc=7, and (e) Uzun [23]

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Fig. 13

Effect of level of VC on normalized Reynolds normal stress σxx profiles: (a) x=120δω(0) and (b) x=210δω(0)

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Fig. 14

Effect of level of VC on normalized Reynolds normal stress σyy profiles: (a) x=120δω(0) and (b) x=210δω(0)

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Fig. 15

Effect of level of VC on normalized Reynolds normal stress σxy profiles: (a) x=120δω(0) and (b) x=210δω(0)

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Fig. 16

(a) Comparison of vorticity thickness development of mixing layer for different levels of VC and (b) vorticity contours (cvc=2), for the refined grid used (1.5 times finer)

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Fig. 17

Effect of level of VC on normalized Reynolds shear stress σxy profiles: (a) x=120δω(0) and (b) x=210δω(0) for the refined grid used (1.5 times finer)

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