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Research Papers: Fundamental Issues and Canonical Flows

# Characteristics of Turbulent Three-Dimensional Wall Jets

[+] Author and Article Information
M. Agelin-Chaab

Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canadaumagelin@cc.umanitoba.ca

M. F. Tachie

Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canada

J. Fluids Eng 133(2), 021201 (Feb 17, 2011) (12 pages) doi:10.1115/1.4003277 History: Received December 22, 2009; Revised November 07, 2010; Published February 17, 2011; Online February 17, 2011

## Abstract

Three-dimensional turbulent wall jet was investigated using a particle image velocimetry technique. Three Reynolds numbers based on the jet exit velocity and diameter of 5000, 10,000, and 20,000 were studied. Profiles of the mean velocities, turbulence intensities, and Reynolds shear stresses as well as two-point velocity correlations and proper orthogonal decomposition analyses were used to document the salient features of the wall jets. The decay and spread rates are independent of Reynolds numbers in the self-similar region. The estimated values of 1.15, 0.054, and 0.255 for the decay rate, wall-normal spread rate, and lateral spread rate, respectively, are within the range of values reported in the literature. The two-point correlation analysis showed that the inclination of the streamwise velocity correlation contours in the inner layer is $11±3 deg$ in the wall region, which is similar to those of canonical turbulent boundary layers. The results from the proper orthogonal decomposition indicate that low-order modes contribute more to the turbulence statistics in the self-similar region than in the developing region. The Reynolds shear stresses are the biggest benefactors of the low-order mode contribution while the wall-normal turbulence intensities are the least.

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## Figures

Figure 3

Profiles of mean velocities and turbulence statistics at selected x/d locations for the different Rej values in the symmetry plane. (a) Streamwise velocity U, (b) streamwise u, and (c) normal v turbulence intensities, and (d) Reynolds shear stresses, uv

Figure 2

Streamwise flow developments. (a) Decay of local maximum mean velocity Um, spread of (b) wall-normal jet half width y0.5 and (c) lateral jet half width z0.5, variation of maximum (d) streamwise turbulence intensity um and (e) wall-normal turbulence intensity vm, and (f) local Reynolds number Rem=Umy0.5/v. AB_1997 is Abrahamsson (1997), P&G_1991 is Padmanabham and Gowda (1991), L&H_2002 is Law and Herlina (2002), and F&S_1989 is Fujisawa and Shirai (1989).

Figure 5

Turbulence intensities and Reynolds shear stresses in both the symmetry and lateral planes. Streamwise turbulence intensities in the (a) symmetry plane and (b) lateral plane, (c) wall-normal turbulence intensities in the symmetry plane, (d) lateral turbulence intensities in the lateral plane, and Reynolds shear stresses in the (e) symmetry plane and (f) lateral plane. AB_1997 is Abrahamsson (1997), S&E_2002 is Sun and Ewing (2002), L&H_2002 is Law and Herlina (2002), P&G_1991 is Padmanabham and Gowda (1991), F&S_1989 is Fujisawa and Shirai (1989), Karl_1993 is Karlsson (1993), and W&F_1969 is Wygnanski and Fiedler (1969).

Figure 4

Profiles of mean velocities in both the symmetry and lateral planes. Streamwise velocity in the (a) symmetry plane and (b) lateral plane, (c) wall-normal velocity in the symmetry plane, and (d) lateral velocity in the lateral plane. AB_1997 is Abrahamsson (1997), S&E_2002 is Sun and Ewing (2002), L&H_2002 is Law and Herlina (2002), P&G_1991 is Padmanabham and Gowda (1991), F&S_1989 is Fujisawa and Shirai (1989), Karl_1993 is Karlsson (1993), and W&F_1969 is Wygnanski and Fiedler (1969).

Figure 15

Profiles of reconstructed turbulent quantities. For the first one and four modes: (a) streamwise turbulence intensities, (c) wall-normal turbulence intensities, and (e) Reynolds shear stresses. For the first 10 and 50 modes: (b) streamwise turbulence intensities, (d) wall-normal turbulence intensities, and (f) Reynolds shear stresses. Symbols for PIV ensemble data: x/d=15 and x/d=65

Figure 14

Contours of Reynolds shear stresses in the developing region ((a) mode 1, (c) mode 4, and (e) mode 10) and in the self-similar region ((b) mode 1, (d) mode 4, and (f) mode 10)

Figure 13

Contours of wall-normal turbulence intensities in the developing region ((a) mode 1, (c) mode 4, and (e) mode 10) and in the self-similar region ((b) mode 1, (d) mode 4, and (f) mode 10)

Figure 12

Contours of streamwise turbulence intensities in the developing region ((a) mode 1, (c) mode 4, and (e) mode 10) and in the self-similar region ((b) mode 1, (d) mode 4, and (f) mode 10)

Figure 11

Fractional turbulence kinetic energy associated with the first few modes for increasing sample size N in the (a) developing region, 12≤x/d≤24; (b) self-similar region, 60≤x/d≤72; (c) developing and self-similar regions with N=1600; and (d) cumulative energy in developing and self-similar regions with N=1600

Figure 10

One-dimensional two-point correlation profiles in the x and z directions from Fig. 9. (a) Ruu(z) and Rww(z) and (b) Ruu(x) and Rww(x)

Figure 9

Contours of two-point correlation for the streamwise (u′) and lateral (w′) fluctuating velocities in the lateral plane at z=0.0 and y=ym. (a) Ruu at x/d=15, (b) Ruu at x/d=65, (c) Rww at x/d=15, and (d) Rww at x/d=65

Figure 8

Streamwise extent of Ruu(Lxuu) and Rvv(Lxvv) and wall-normal extent of Ruu(Lyuu) and Rvv(Lyvv). (a) Lxuu and (b) Lxvv, Lyuu, and Lyvv

Figure 7

One-dimensional two-point correlation profiles extracted along the vertical and horizontal dashed lines in Fig. 6. (a) Ruu(y) and Rvv(y) and (b) Ruu(x) and Rvv(x)

Figure 6

Contours of two-point correlation for the streamwise (u′) and wall-normal (v′) fluctuating velocities in the symmetry plane at y/ym=0.56. (a) Ruu at x/d=15, (b) Ruu at x/d=65, (c) Rvv at x/d=15, and (d) Rvv at x/d=65

Figure 1

(a) A sketch of a turbulent three-dimensional wall jet; schematic of the test section showing arrangement of PIV system for measurements in the jet (b) symmetry plane and (c) lateral plane at y=ym

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