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Research Papers: Fundamental Issues and Canonical Flows

RANS Modeling of Accelerating Boundary Layers

[+] Author and Article Information
Ugochukwu R. Oriji, Sahand Karimisani, Paul G. Tucker

Department of Engineering,
University of Cambridge,
Cambridge CB2 1TN, UK

The energy budgets for the LS model are presented in the Appendix.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 4, 2013; final manuscript received June 7, 2014; published online September 10, 2014. Assoc. Editor: Sharath S. Girimaji.

J. Fluids Eng 137(1), 011202 (Sep 10, 2014) (9 pages) Paper No: FE-13-1702; doi: 10.1115/1.4027846 History: Received December 04, 2013; Revised June 07, 2014

A numerical investigation of accelerated boundary layers (BL) has been performed using linear and nonlinear eddy viscosity models (EVM). The acceleration parameters (KS) investigated the range between 1.5 × 10−6 and 3.0 × 10−6. The one-equation (k-l), Spalart Allmaras (SA), and the two-equation Menter Shear Stress Transport (SST) and Chien models in their standard forms are found to be insensitive to acceleration. Nevertheless, proposed modifications for the SA, Chien, and the k-l models significantly improved predictions. The major improvement was achieved by modifying the damping functions in these models and also an analogous source term, E, for the Chien model. Encouraging agreement with measurements is found using the Launder Sharma (LS), cubic and explicit algebraic stress models (EASM) in their standard forms. The cubic model best predicted the turbulence quantities. Investigations confirm that it is practical for Reynolds-Average Navier–Stokes (RANS) models to capture reversion from the turbulent to laminar state albeit for equilibrium sink type flows.

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Figures

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Fig. 1

Launder and Jones [13] correlation trend and excellent agreement with data obtained from other acceleration parameters

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Fig. 2

Schematic of geometry

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Fig. 3

Mean velocity profile in a sink-flow with KS = 1.5 × 10−6 at x ≈ 2.7 m

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Fig. 4

Mean velocity profile in a sink-flow with KS = 2.5 × 10−6 at x ≈ 2.7 m

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Fig. 5

Mean velocity profile in sink-flow for KS = 2.5 × 10−6 at x ≈ 2.7 m

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Fig. 6

Axial variation of H and KS for LS model for KS = 3.86 × 10−6

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Fig. 7

Variation of H with KS for sink-flow turbulent BLs

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Fig. 8

Cross stream variation of normalized turbulence kinetic energy at KS = 1.5 × 10−6

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Fig. 9

Cross stream variation of normalized turbulence dissipation rate at KS = 1.5 × 10−6

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Fig. 10

Dimensionless normal Reynolds stress in a FPG flow with KS = 1.5 × 10−6

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Fig. 11

Dimensionless normal Reynolds stress in a FPG flow with KS = 1.5 × 10−6

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Fig. 12

Dimensionless normal Reynolds stress in a FPG flow with KS = 1.5 × 10−6

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Fig. 13

Normalized turbulence kinetic energy at KS = 2.5 × 10−6

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Fig. 14

Normalized turbulence dissipation rate at KS = 2.5 × 10−6

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Fig. 15

Dimensionless normal Reynolds stress in a FPG flow with KS = 2.5 × 10−6

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Fig. 16

Dimensionless normal Reynolds stress in a FPG flow with KS = 2.5 × 10−6

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Fig. 17

Dimensionless normal Reynolds stress in a FPG flow with KS = 2.5 × 10−6

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Fig. 18

A+ modification of k-l model for a sink-flow with KS = 1.5 × 10−6 at x ≈ 2.7 m

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Fig. 19

Impact of fμ modification in k-ε Chien model for a sink-flow at KS = 1.5 × 10−6 at x ≈ 2.7 m

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Fig. 20

Impact of fμ modification in k-ε Chien model for a sink-flow at KS = 2.5 × 10−6 at x ≈ 2.7 m

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Fig. 21

Impact of modification of the k-ε Chien model to include E term for a sink-flow at KS = 1.5 × 10−6 at x ≈ 2.7 m

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Fig. 22

Impact of modification of the k-ε Chien model to include E term for a sink-flow at KS = 2.5 × 10−6 at x ≈ 2.7 m

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Fig. 23

Log mean velocity profiles for KS = 1.5 × 10−6 for the modified (methods 1 and 2) and the standard SA models

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Fig. 24

Log mean velocity profile for KS = 2.5 × 10−6 for the modified (methods 1 and 2) and the standard SA model

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Fig. 25A

Turbulent kinetic energy budget for KS = 0 (black lines) and KS = 2.5 × 10−6 (gray lines)

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