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Research Papers

Simulation of Rotating Channel Flow With Heat Transfer: Evaluation of Closure Models

[+] Author and Article Information
Alan S. Hsieh

Department of Aerospace Engineering Sciences,
University of Colorado,
Boulder, CO 80309
e-mail: alan.hsieh@colorado.edu

Sedat Biringen

Department of Aerospace Engineering Sciences,
University of Colorado,
Boulder, CO 80309
e-mail: sedat.biringen@colorado.edu

Alec Kucala

Department of Aerospace Engineering Sciences,
University of Colorado,
Boulder, CO 80309
e-mail: alec.kucala@colorado.edu

1Corresponding author.

Manuscript received September 14, 2015; final manuscript received April 12, 2016; published online May 24, 2016. Assoc. Editor: Graham Pullan.

J. Turbomach 138(11), 111009 (May 24, 2016) (15 pages) Paper No: TURBO-15-1203; doi: 10.1115/1.4033463 History: Received September 14, 2015; Revised April 12, 2016

A direct numerical simulation (DNS) of spanwise-rotating turbulent channel flow was conducted for four rotation numbers: Rob=0, 0.2, 0.5, and 0.9 at a Reynolds number of 8000 based on laminar centerline mean velocity and Prandtl number 0.71. The results obtained from these DNS simulations were utilized to evaluate several turbulence closure models for momentum and heat transfer transport in rotating turbulent channel flow. Four nonlinear eddy viscosity turbulence models were tested and among these, explicit algebraic Reynolds stress models (EARSM) obtained the Reynolds stress distributions in best agreement with DNS data for rotational flows. The modeled pressure–strain functions of EARSM were shown to have strong influence on the Reynolds stress distributions near the wall. Turbulent heat flux distributions obtained from two explicit algebraic heat flux models (EAHFM) consistently displayed increasing disagreement with DNS data with increasing rotation rate.

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References

Figures

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Fig. 1

Geometry of DNS computational domain for turbulent channel flow with rotation in the spanwise direction

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Fig. 2

One-dimensional energy spectra along the streamwise axis for case A (Rob=0). Solid: Euu; dash-dot: Evv; dotted: Eww; and dashed: Kolmogorov −5/3 spectrum.

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Fig. 3

Verification of DNS data for case A (Rob=0): (a) (u1′u1′¯+)1/2, (b) (u2′u2′¯+)1/2, (c) (u3′u3′¯+)1/2, and (d) u1′u2′¯+. Black: DNS; red: Kasagi and Nishino [18]; and square: Kreplin and Eckelmann [17].

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Fig. 4

Mean velocity distributions with 2Ω lines for full simulation cases A–D. Black: case A (Rob=0); red: case B (Rob=0.2); blue: case C (Rob=0.5); and magenta: case D (Rob=0.9). −−−: 2Ω lines.

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Fig. 5

Mean temperature distributions for full simulation cases A–D. Black: case A (Rob=0); red: case B (Rob=0.2); blue: case C (Rob=0.5); and magenta: case D (Rob=0.9).

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Fig. 6

Instantaneous ωx′ map for a y–z section at x=2π: (a) case A (Rob=0), (b) case B (Rob=0.2), and (c) case C (Rob=0.5)

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Fig. 7

Time-averaged v and w velocity vectors for a y–z section at x=2π: (a) case A (Rob=0), (b) case B (Rob=0.2), and (c) case C (Rob=0.5)

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Fig. 8

Modeled Reynolds stress profiles for case D (Rob=0.9): (a) u1′u1′¯+, (b) u2′u2′¯+, (c) u3′u3′¯+, and (d) u1′u2′¯+. Black: DNS; red: linear eddy viscosity model [20]; and blue: nonlinear eddy viscosity model [8].

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Fig. 9

Modeled Reynolds stress profiles for case A (Rob=0): (a) u1′u1′¯+, (b) u2′u2′¯+, (c) u3′u3′¯+, and (d) u1′u2′¯+. Black: DNS; blue: PRDO; green: SG; red: GI; and magenta: GWJ.

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Fig. 10

Modeled Reynolds stress profiles for case B (Rob=0.2): (a) u1′u1′¯+, (b) u2′u2′¯+, (c) u3′u3′¯+, and (d) u1′u2′¯+. Black: DNS; blue: PRDO; green: SG; red: GI; and magenta: GWJ.

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Fig. 11

Modeled Reynolds stress profiles for case C (Rob=0.5): (a) u1′u1′¯+, (b) u2′u2′¯+, (c) u3′u3′¯+, and (d) u1′u2′¯+. Black: DNS; blue: PRDO; green: SG; red: GI; and magenta: GWJ.

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Fig. 12

Modeled Reynolds stress profiles for case D (Rob=0.9): (a) u1′u1′¯+, (b) u2′u2′¯+, (c) u3′u3′¯+, and (d) u1′u2′¯+. Black: DNS; blue: PRDO; green: SG; red: GI; and magenta: GWJ.

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Fig. 13

Modeled pressure–strain budget term profiles for case A (Rob=0): (a) Π11, (b) Π22, (c) Π33, and (d) Π12. Black: DNS; red: SG; and blue: GI.

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Fig. 14

Modeled pressure–strain budget term profiles for case B (Rob=0.2): (a) Π11, (b) Π22, (c) Π33, and (d) Π12. Black: DNS; red: SG; and blue: GI.

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Fig. 15

Modeled turbulent heat flux profiles for cases A (Rob=0) and B (Rob=0.2): (a) u1′θ′¯+ (case A), (b) u2′θ′¯+ (case A), (c) u1′θ′¯+ (case B), and (d) u2′θ′¯+ (case B). Black: DNS; red: YWL; and blue: SA.

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Fig. 16

Modeled turbulent heat flux profiles for cases C (Rob=0.5) and D (Rob=0.9): (a) u1′θ′¯+ (case C), (b) u2′θ′¯+ (case C), (c) u1′θ′¯+ (case D), and (d) u2′θ′¯+ (case D). Black: DNS; red: YWL; and blue: SA.

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Fig. 17

Modeled pressure–temperature gradient profiles for cases A (Rob=0) and B (Rob=0.2): (a) Π1θ (case A), (b) Π2θ (case A), (c) Π1θ (case B), and (d) Π2θ (case B). Black: DNS; red: YWL; and blue: SA.

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