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Research Papers: Fundamental Issues and Canonical Flows

# Spectral Linear Stochastic Estimation of the Turbulent Velocity in a Square Three-Dimensional Wall Jet

[+] Author and Article Information
Joseph W. Hall

Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, E3B 5A3, Canadajwhall@unb.ca

Daniel Ewing

J. Fluids Eng 132(5), 051203 (Apr 28, 2010) (9 pages) doi:10.1115/1.4001490 History: Received June 08, 2009; Revised March 16, 2010; Published April 28, 2010; Online April 28, 2010

## Abstract

The instantaneous turbulent velocity field in a three-dimensional wall jet was estimated from the fluctuating wall pressure using a spectral linear stochastic estimation technique. The wall jet investigated issued from a long square channel with Reynolds number of 90,000. Two downstream positions in the intermediate field were examined, $x/h=10$ and $x/h=20$, owing to the rapid changes in wall jet development over this region. The results indicate that the passage of the large-scale structures cause large, coherent lateral sweeps of fluid across the entire span of the wall jet. These sweeps are caused by the passage of half horseshoe-like structures and appear to be responsible for the larger lateral development of this flow.

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## Figures

Figure 1

Schematic of a three-dimensional wall jet

Figure 2

Contours of (a) U/Umax, (b) urms/Umax, (c) W/Umax, and (d) wrms/Umax at x/h=10

Figure 3

Contours of (a) U/Umax, (b) urms/Umax, (c) W/Umax, and (d) wrms/Umax at x/h=20

Figure 4

Relative and cumulative pressure energy recovered using the POD integrated over all frequencies

Figure 5

POD results at x/h=10

Figure 6

POD results at x/h=20

Figure 7

Estimate of the streamwise (left) and lateral (right) component of the velocity in the y−z plane at x/h=10. The streamwise direction is into the page.

Figure 8

Estimate of the streamwise (left) and lateral (right) component of the velocity in the y−z plane at x/h=20. The streamwise direction is into the page.

Figure 9

A typical sequence of the streamwise (left) and the lateral (right) velocity estimates from first two POD modes including mean in the y−z plane at x/h=10. The streamwise direction is into the page.

Figure 10

A typical sequence of the streamwise (left) and the lateral (right) velocity estimates from first two POD modes including mean in the y−z plane at x/h=20. The streamwise direction is into the page.

Figure 11

Isosurface at ±1 for ∂(W+west)/∂y for wall jet at x/h=10

Figure 12

Isosurface at ±1 for ∂(W+west)/∂y for wall jet at x/h=20

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