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Research Papers: Flows in Complex Systems

# Measurements of a Wall Jet Impinging Onto a Forward Facing Step

[+] Author and Article Information
D. C. Langer, D. J. Wilson

Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 2G8, Canada

B. A. Fleck

Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 2G8, Canadabrian.fleck@ualberta.ca

J. Fluids Eng 131(9), 091103 (Aug 18, 2009) (9 pages) doi:10.1115/1.3203201 History: Received September 09, 2008; Revised June 29, 2009; Published August 18, 2009

## Abstract

This study examines a horizontal wall jet impinging onto a forward facing vertical step in a cross-flow. Planar laser induced fluorescence (PLIF) experiments in a $68×40 mm2$ water channel indicate how the wall-jet flow after impinging onto the step becomes a vertical jet with an elliptical cross section. This study proposes predictive empirical correlations for the aspect ratio and perimeter of the jet’s elliptical cross section based on the step geometry and the inlet flow conditions. A numerical model is also presented, which was produced from a commercial Reynolds averaged Navier–Stokes computational fluid dynamics (CFD) code with the $k-ϵ$ closure model. The experimental results were well represented by correlations for the perimeter $P$ and aspect ratio $S$ using the parameters $H$ (the step height), $L∘$ (the distance from the jet represented as a point source to the step), and $R$ (the velocity ratio). The CFD simulation was able to predict the trends in the perimeter (under different conditions), aspect ratio, and the shape of the concentration profile, but overpredicted the jet’s perimeter by approximately 50%. The results of these tests are required as input parameters when modeling jet trajectories.

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## Figures

Figure 1

Schematic of the test section. The step height (H), the effective distance (L), and the velocity ratio (R=Vjet/V∞) were varied for the parametric study. The shape of the cross section perpendicular to the direction of the jet is shown at three locations: the pipe exit (a), the top of the step (b), and downstream of the step (c). The round jet flattens at the step (b) and forms a high aspect ratio ellipse which then “rolls-up” to become more circular.

Figure 2

Schematic of the experimental apparatus. The laser beam is steered into a cylindrical focusing lens through the use of two focusing mirrors. The beam then travels into a Powell lens forming a laser sheet. The camera is oriented perpendicularly to the laser sheet and located above the water channel. A sheet of glass is used at the top of the water surface to remove the distortions caused by waves within the channel.

Figure 3

Single experimental image of the concentration profile within the jet. A linear concentration scale is shown in (a) and a sawtooth scale used to emphasize the structures apparent in the jet is shown in (b). The cross-flow moves from left to right, with the jet fluid moving out of the page. The step is located at 0 mm.

Figure 4

Experimental ((a) and (b)) and CFD ((c) and (d)) concentration profiles. Linear and sawtooth concentration scales are shown so flow structures can be compared. The cross-flow moves from left to right with the jet fluid moving out of the page. The step is located at 0 mm.

Figure 5

Measured concentrations along the maximum depth line (a) and the maximum width line (b). The horizontal line shows the 70% value where the depth and width are measured. A threshold value of 60% of the maximum concentration was used to determine the Gaussian fit.

Figure 6

Physical definitions in the CFD code. Dimensions were chosen to match the water channel facility used for the experiments (a). The type and locations of the boundary conditions are given in (b). The coarse mesh, which was used for the simulations (with the exception of the grid refinement study), is given viewed along the symmetry plane in (c).

Figure 7

Variation in ϕ, the blending factor used in the CFD code, where ϕ=0 represents a first order method and ϕ=1 represents a second order method. Values are for the vertical velocity along the major axis of the elliptical cross section in the measurement plane. The global order of the solution was found to be 1.2, which corresponds to a ϕ value of approximately 0.2.

Figure 8

Measured values of perimeter compared with the different inlet conditions, normalized with the jet diameter d. The effect of the step position (L) with different velocity ratios and a constant step height is shown in (a). The effect of the step height (H) at different velocity ratios is shown in (b). The effect of velocity ratio R for a single step height and length is shown in (c).

Figure 9

Measured perimeters compared with the experimental fit outlined in Eq. 6. The error bars represent twice the standard deviation of the condition where five tests were taken.

Figure 10

Experimental correlation for the jet aspect ratio S (defined in Eq. 7) based on the step height H, effective distance to the step L∘, and velocity ratio R

Figure 11

Comparison of CFD results to experimental results using the scaling relation given in Eq. 6. CFD results slightly overpredict the perimeter due to the artificial viscosity introduced into the flow by the k-ϵ turbulence model and the low order of the simulation.

Figure 12

Comparison of aspect ratio measurements S for CFD results and experimental results in terms of the step height H, effective distance to the step (L∘), and velocity ratio R

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