Research Papers: Fundamental Issues and Canonical Flows

Rough Surface Wall Function Treatment With Single Equation Turbulence Models

[+] Author and Article Information
U. Goldberg

Metacomp Technologies Inc.,
28632 Roadside Drive,
Agoura Hills, CA 91301
e-mail: ucg@metacomptech.com

P. Batten

Metacomp Technologies Inc.,
28632 Roadside Drive,
Agoura Hills, CA 91301

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 3, 2016; final manuscript received February 13, 2017; published online June 2, 2017. Assoc. Editor: Daniel Livescu.

J. Fluids Eng 139(8), 081204 (Jun 02, 2017) (11 pages) Paper No: FE-16-1649; doi: 10.1115/1.4036245 History: Received October 03, 2016; Revised February 13, 2017

Most literature in the area of turbulent flow over rough surfaces discusses methods for turbulence models based on two or more transport equations, one of which is that for turbulence kinetic energy which supplies k that is heavily used for the rough wall treatment. However, many aeronautical engineers routinely use single equation turbulence models which solve directly for eddy viscosity and do not involve k. The present work proposes methods by which such one-equation models can predict flow cases which include multiple rough surfaces. The current approach does not impose changes to the wall distance function, should such a function be necessary. Several examples show that the proposed method is able to produce good predictions of both skin friction and heat transfer along rough surfaces. While results are not always as accurate as those predicted by turbulence models which solve for k, especially if detached or wake-like flow regions exist, accompanied by a significant increase in eddy viscosity, the single-equation models are able to provide predictions at least good enough for preliminary studies.

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Fig. 1

S–A ν̃,νt versus y+

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Fig. 2

Comparison of S–A and Rt model predictions with correlations for Cf along a rough flat plate at M = 0.84 and y1+ = 7 (P–S roughness model)

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Fig. 3

Performance of Pisarenco et al. [4] roughness model along a rough pipe

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Fig. 6

(a) Topology and dimensions and (b) grid

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Fig. 7

Streamwise velocity profiles at three locations on lower (rough) wall

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Fig. 8

Basic nomenclature

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Fig. 4

(Top) Sand dune mesh and (bottom) x-velocity contours showing the separation zone

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Fig. 5

(L) Signed friction speed predicted by Rt, S–A, and k–ε and (R) Rt residuals

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Fig. 16

(a) Partial mesh and (b) near-wall grid detail

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Fig. 12

(a) Computational domain and (b) μt/μ contours along curved wall

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Fig. 13

Heat transfer coefficient along the straight and curved wall sections

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Fig. 14

Grid convergence test for curved wall case

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Fig. 15

Main features and dimensions

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Fig. 9

Heated rough cylinder in crossflow (air flow from right to left)

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Fig. 10

KS = 1.35 mm: (a) Heat transfer from cylinder surface at midspan and (b) μt/μ contours

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Fig. 11

Predictions for a cooled rough flat plate by one-equation models: (L) Stanton no. and (R) Cf

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Fig. 17

Mach contours in leading edge region

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Fig. 18

μt kicked on due to the trip

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Fig. 19

Predicted velocity profiles (u+ versus y+) at x = 391 mm with ∂p/∂s active in the wall function

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Fig. 20

Predicted velocity profiles with ∂p/∂s active, compared to experimental data at x = 391 mm




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