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Research Papers: Techniques and Procedures

The Effects of Inflow Uncertainties on the Characteristics of Developing Turbulent Flow in Rectangular Pipe and Asymmetric Diffuser

[+] Author and Article Information
Saeed Salehi

Hydraulic Machinery Research Institute,
School of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 11155-4563, Iran
e-mail: s.salehi@ut.ac.ir

Mehrdad Raisee

Associate Professor
Hydraulic Machinery Research Institute,
School of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 11155-4563, Iran
e-mail: mraisee@ut.ac.ir

Michel J. Cervantes

Professor
Division of Fluid and Experimental Mechanics,
Luleå University of Technology,
Luleå 97187, Sweden;
Department of Energy and Process Engineering,
Water Power Laboratory,
Norwegian University of Science and Technology,
Trondheim 7491, Norway
e-mail: michel.cervantes@ltu.se

Ahmad Nourbakhsh

Professor
Hydraulic Machinery Research Institute,
School of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 11155-4563, Iran
e-mail: anour@ut.ac.ir

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 9, 2016; final manuscript received November 15, 2016; published online February 20, 2017. Assoc. Editor: Alfredo Soldati.

J. Fluids Eng 139(4), 041402 (Feb 20, 2017) (19 pages) Paper No: FE-16-1151; doi: 10.1115/1.4035302 History: Received March 09, 2016; Revised November 15, 2016

In the current paper nondeterministic computational fluid dynamics (CFD) computations of three-dimensional (3D), developing, and statistically steady turbulent flow through an asymmetric diffuser with moderate adverse pressure gradient are presented. The inflow condition is assumed to be uncertain. The inlet streamwise velocity is supposed to be a stochastic process and described by the Karhunen–Loève (KL) expansion. In addition, the inlet turbulence intensity and turbulent length scale are assumed to be uncertain. The nonintrusive polynomial chaos (NIPC) expansion is used to propagate the inflow uncertainties in the flow field. The developed code is verified using a Monte Carlo (MC) simulation with 1000 Latin Hypercube samples on a planar asymmetric diffuser. A very good agreement is observed between the results of MC and polynomial chaos expansion methods. The verified uncertainty quantification method is then applied to stochastic developing turbulent flow through a 3D asymmetric diffuser. It was observed that the eigenvalues of covariance kernel rapidly decay due to the large correlation lengths and thus a few terms in the truncated KL expansion are used to describe the stochastic inlet velocity. For the KL expansion, the mean and the standard deviation are set to those measured experimentally. The uncertain inlet condition has a significant influence on the numerical results of velocity and turbulence fields specially in the developing region before the shear layers meet. It is concluded that one of the reasons for discrepancies between experimental and deterministic CFD results is the uncertainty in inflow condition. A sensitivity analysis is also performed using the Sobol’ indices and contribution of each uncertain parameter on outputs variance is presented.

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Figures

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Fig. 1

(a) Experimental setup used by Cervantes and Engström [27] (dimensions in mm) and (b) 2D view of the computational domain

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Fig. 2

(a) The locations of available experimental data at section x = 100 mm, (b) and (c) 3D surfaces fitted to the experimental data (in (b) and (c) nodes represent the experimental data)

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Fig. 3

(a) Schematic of Obi diffuser, Buice and Eaton [41] and (b) computational grid

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Fig. 4

PDF of Reynolds number for Obi diffuser

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Fig. 5

Comparison of NIPC and MC results (mean and ±2σ range) for stochastic turbulent flow through Obi diffuser: (a) streamwise velocity profiles and (b) streamwise normal Reynolds stress

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Fig. 6

Comparison of NIPC and MC results (mean and ±2σ range) of skin friction and pressure coefficients on the diffuser walls: (a) skin friction coefficient on upper wall, (b) skin friction coefficient on lower wall, (c) pressure coefficient on upper wall, and (d) pressure coefficient on lower wall

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Fig. 7

PDF and CDF of pressure coefficient at two points on lower wall of diffuser (point 1 at x/H = 0 and point 2 at x/H = 21): (a) point 1 and (b) point 2

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Fig. 8

Contours of mean and standard deviation of normalized streamwise velocity: (a) mean and (b) standard deviation

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Fig. 10

Eigenfunctions corresponding to the first six terms in KL expansion for the exponential kernel

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Fig. 9

Eigenvalues for the exponential kernel

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Fig. 11

Results of grid independency study, (a) U, (b) u2¯, and (c) v2¯

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Fig. 12

Effect of polynomial order (p) on accuracy of results: (a) PDF of streamwise velocity and (b) PDF of streamwise component of normal Reynolds stress

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Fig. 13

Development of (a) streamwise velocity, (b) u2¯, and (c) v2¯ along centerline with ±2σ bounds

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Fig. 14

Contours of mean and standard deviation of the streamwise velocity on the symmetry plane: (a) mean and (b) standard deviation

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Fig. 15

Contours of mean and standard deviation of the Reynolds stresses on the symmetry plane: (a) u2¯ mean, (b) u2¯ standard deviation, (c) v2¯ mean, (d) v2¯ standard deviation, (e) uv¯ mean, and (f) uv¯ standard deviation

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Fig. 16

Contours of mean and standard deviation of the static pressure on the symmetry plane: (a) mean and (b) standard deviation

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Fig. 17

Development of the pressure coefficient along upper wall with ±2σ bounds

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Fig. 18

Sobol’ indices of centerline velocity and Reynolds stresses: (a) U, (b) u2¯, and (c) v2¯

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Fig. 19

Contours of Sobol’ indices on symmetry plane: (a) S1 of U, (b) S5 of U, (c) S6 of U, (d) S1 of u2¯, (e) S5 of u2¯, and (f) S6 of u2¯

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Fig. 20

Profiles of (a) streamwise and (b) normal velocity in three sections of diffuser

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Fig. 21

Contours of streamwise velocity in three section of diffuser: (a) mean in section 2082 mm, (b) standard deviation in section 2082 mm, (c) mean in section 2357 mm, (d) standard deviation in section 2357 mm, (e) mean in section 2632 mm, and (f) standard deviation in section 2632 mm

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Fig. 22

Profiles of Reynolds stresses in three sections of diffuser: (a) u2¯, (b) v2¯, and (c) uv¯

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