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Research Papers: Forced Convection

Dissimilarity of Turbulent Fluxes of Momentum and Heat in Perturbed Turbulent Flows

[+] Author and Article Information
H. D. Pasinato

Department of Chemical Engineering,
FRN, Universidad Tecnológica Nacional,
Avda. P. Rotter s/n,
8318 Plaza Huincul, Argentina
e-mail: hpasinato@frn.utn.edu.ar

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 20, 2012; final manuscript received December 28, 2012; published online April 11, 2013. Assoc. Editor: W. Q. Tao.

J. Heat Transfer 135(5), 051701 (Apr 11, 2013) (12 pages) Paper No: HT-12-1297; doi: 10.1115/1.4023358 History: Received June 20, 2012; Revised December 28, 2012

The dissimilarity between the Reynolds stresses and the heat fluxes in perturbed turbulent channel and plane Couette flows was studied using direct numerical simulation. The results demonstrate that the majority of the dissimilarity was due to the difference between the wall-normal fluxes, while the difference between the streamwise fluxes was lower. The main causes for the dissimilarity were the production terms, followed by the velocity-pressure interaction terms. Further insights into the importance of the velocity-pressure interaction in the origin of the dissimilarity are provided using two-point correlation. Furthermore, an octant conditional averaged dataset reveals that not only the wall-normal heat flux but also the streamwise heat flux is strongly related to the wall-normal gradient of the mean temperature. A simple Reynolds-averaged Navier–Stokes (RANS) heat flux model is proposed as a function of the Reynolds stresses. A comparison of the direct numerical simulation data with an “a priori” prediction suggests that this simple model performs reasonably well.

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Figures

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Fig. 1

Scheme of parallel DNS for a numerical experiment of perturbed turbulent flow

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Fig. 2

U (filled symbols) and Θ (open symbols) for (a) channel and (b) Couette flow, perturbed with blowing ((a)–(a) and (b)–(a)) and an APGS ((a)–(b) and (b)–(b)), at two different locations: (squares) on the slot; (stars) at W+ downstream from the slot. Open and filled circles U and Θ for nonperturbed flow, respectively. Solid line, law of the wall, (1/041)ln(y+) + 50. Note the shift for APGS.

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Fig. 3

Φ balance for perturbed channel flow for y+≃38, cases (a) CHB6220; (b) CHS6220; (c) CHABR220; and (d) CHFBR220. Solid line, DΦ/Dt; – – –, diffusion; filled stars, turbulent fluxes; □·□·□, (Sm-Se) as in Eq. (4); °·°·°, balance. Note the different scales. Solid vertical lines denote the slot location, vertical dotted lines denote sections W+ and 5W+ from the slot.

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Fig. 4

Idem to Figs. 3(a)3(d) for perturbed Couette flow, cases (a) CFB6590; (b) CFS590; (c) CFABR590; and (d) CFFBR590. Note the different scales.

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Fig. 5

Contribution of (a) ∂(〈uu〉-〈θu〉)/∂x and (b) ∂(〈uv〉-〈θv〉)/∂y to DΦ/Dt for four positions from the wall for channel flow perturbed with blowing. Solid line, y+≃5; –. –. –, y+≃18; □·□·□, y+≃38; °·°·°, y+≃137. Note the different scales.

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Fig. 6

Budget of (a)–(c)〈φu〉 and (b)–(d)〈φv〉 balances at y+ = 38 for (a)–(b) channel flow perturbed with blowing and (c)–(d) Couette flow perturbed with an APGS. °·°·°, balance; solid line, D(φu)/Dt and D(φv)/Dt; – – –, diffusion; ⋆·⋆·⋆, production; •·•·•, turbulent transport; –. –. –, dissipation; □·□·□, velocity-pressure interaction. Note the different scales.

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Fig. 7

Contribution to differences 〈φu〉 and 〈φv〉 by turbulence production for channel flow perturbed with an APGS at y+=38. ⋆·⋆·⋆, total; solid line, function of mean-field dissimilarity; – – –, function of turbulence dissimilarity.

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Fig. 8

(a)–(a)〈u∂p/∂x〉; (a)-(b)〈θ∂p/∂x〉; (b)-(a)〈v∂p/∂x〉; and (b)–(b)〈v∂p/∂y〉 for channel flow perturbed with blowing. Solid line, on the slot; –. –. –, W+ and,., 5W+ downstream from the slot; °·°·°, nonperturbed flow (note the shift in the abscissa for plots (a)–(b) and (b)–(a)).

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Fig. 9

Total (open symbol) and in (Q2 + Q4) (filled symbol) of (a)〈v∂p/∂x〉 and (b)〈v∂p/∂y〉 for channel flow perturbed with blowing, at y+ equal to 5, 16, 38, and 137 from the wall. Squares, on the slot; diamonds, W+; stars, 5W+ downstream from the slot; circles, nonperturbed flow.

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Fig. 10

(a) Instantaneous pressure field; (b) two-point correlation for 〈v∂p/∂x〉; and (c) 〈v∂p/∂y〉, for channel flow perturbed with blowing, for quadrant Q4 at (rx+,y+) plane (rz+=0). Contour levels are for: (a) range (–0.50; 0.14), increments 0.1; (b)–(c) (–0.10; 0.05), 0.01. Solid line, positive and dotted line, negative. Dots denote detection point at W+ from slot and at y+=38 from the wall.

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Fig. 11

(a)〈uθ〉oct/〈uθ〉 and (b)〈vθ〉oct/〈vθ〉 for channel flow perturbed with blowing, on the slot ((a)–(a); (b)–(a)), at W+ downstream ((a)–(b); (b)–(b)), and at 5W+ downstream ((a)–(c); (b)–(c)). Open diamonds Q11;u>0,v>0,θ>0; filled diamonds Q12;u>0,v>0,θ<0; open squares Q22;u<0,v>0,θ<0; filled squares Q21;u<0,v>0,θ>0; open stars Q32;u<0,v<0,θ<0; filled stars Q31;u<0,v<0,θ>0; open circles Q41;u>0,v<0,θ>0; filled circles Q42;u>0,v<0,θ<0.

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Fig. 12

(a) θrms/urms and (b) (∂Θ/∂y)/(∂U/∂y) for channel flow perturbed with blowing. Filled circles developed values; °·°·°, on the slot; □·□·□, W+; ⋆·⋆·⋆, 5W+ downstream.

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Fig. 13

Reynolds stress 〈uu〉 and 〈uv〉; solid line, on the slot; – – –, W+; –. –. –, 5W+, and a prior comparison of RANS model with DNS data for turbulent heat fluxes 〈uθ〉 and 〈vθ〉, for channel flow perturbed with (a) blowing and (b) an APGS. Open symbols, DNS data; filled symbols, a priori RANS prediction. Squares, on the slot; diamonds, W+; stars, 5W+ downstream; °·°·°, nonperturbed values of turbulent heat fluxes.

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