1. A comparative study of plane and radial turbulent wall jets
Speaker: William Lin
Advisor: Prof. Eric Savory
Affiliation:
Good afternoon. I will be speaking about velocity measurements of turbulent steady wall jets. Two common wall jet configurations are the plane and radial ones and our work compares their characteristics. I am one of the workers in the AFM research group. My advisor for this work is Prof. Eric Savory. The work in this presentation is made possible by the sponsors shown.
Sponsors:

2. Outline 1. Introductory remarks Overview of two configurations
Motivation
Objectives
2. Plane wall jet velocity measurements
3. Comparison of plane and radial wall jets
4. Closing remarks
I’ll start this talk with remarks on the objectives of the work, our motivations for studying this flow, and a basic description of the phenomenon of interest. Then we’ll be ready to talk about the experimental setup, measurement apparatus, and uncertainty analysis of our plane wall jet experiment. The results consist of normal-to-wall profiles of velocity, and characterization of the jet development by the jet spread and velocity decay rates. We then compare the wall jet results in the plane configuration with those from the radial configuration. The closing remarks consist of conclusions and suggestions for future work.

3. Brief overview of the plane wall jet
Open slot top
Open exit Y
In the plane wall jet, momentum is introduced at a two-dimensional slot nozzle. The width of the initial jet is traditionally denoted as b. The dominant flow is tangential to the wall of interest. With increasing downstream distance from the slot exit, the streamwise velocity decays and the jet spreads in the direction normal to the wall. The downstream velocity profile develops from the initial slot jet to the downstream profile shown, which is the distinguishing feature of a wall jet. This characteristic velocity profile attains a maximum value between the wall and the outer flow. The inner and outer layers of the wall jet resemble a boundary layer and a free shear flow, respectively.
Other aspects of the flow geometry are varied in previous studies. t is the slot top thickness. In the present work, because we are interested in the option of introducing a co-flow, the t/b ratio is very small. A wide range of t/b ratios can be found in the literature. Numerical studies usually invoke a closed off slot top because this is an easier boundary condition to apply than one that is open. However, if there is a top wall as well, the closed configuration may lead to undesirable recirculation in the flow domain.
The flow is confined with side walls to negate the effect of external disturbances. There may or may not be a top wall in previous studies. No top wall allows maximum entrainment of external air and jet growth, but it is more difficult to minimize disturbances with an open condition. For our experiments, we enclose the flow domain at the top. t
Outer layer
Inner layer b

4. Brief overview of the radial wall jet
nozzle ½D
Axis of symmetry
Open exit yD
Now, we look at the radial wall jet. Here the flow momentum is added as a round jet that impinges normal to a wall. After a transition region where the dominant flow direction changes from normal to tangential to the wall, a wall jet develops, where we see the characteristic wall jet streamwise velocity profile. Parameters to note here are nozzle diameter D and the nozzle distance from the wall. y r
impingement regime
wall jet regime

5. Motivation Applications: heating/cooling or drying/wetting
removal or deposition of particles/films
protective fluid layer
modelling of storm outflows
We’re motivated to study turbulent wall jets because they are widely used in industrial applications to heat or cool, or dry or wet a solid surface and they are used for the removal or deposition of substances on a solid surface. As a thin fluid layer adjacent to a wall, wall jets can be used to protect the wall from damaging temperatures or substances. Furthermore, we observe wall jets in atmospheric flows such as the cold air gust front that precedes a storm, convective downdraft outflows.

6. Objectives
To take velocity measurements of the plane turbulent wall jet
To compare available experimental results from plane and radial wall jets.
Our main objectives are as follows. We wish to physically investigate the velocity characteristics of a plane turbulent wall jet under particular conditions not treated in the literature. Parameters such as the slot top thickness and top boundary height have not been rigorously examined previously. We also wish to compare and draw conclusions from available experimental results for the two configurations.

7. Co-ordinate system V Y Z y z x W U
It’s useful to provide a few definitions before proceeding. We define the origin of the co-ordinate system at the slot exit and wall. Plane wall jet results to be shown are along the centreline of the domain. The dominant flow direction, normal-to-wall direction, and spanwise directions are denoted as lower-case x, y, and z, respectively. <click>The distance between the side walls is defined as upper-case Z. <click> The distance from the wall to the top wall is defined as upper-case Y.
Upper-case U, V, W are the time-averaged flow velocities in the x, y, z directions, respectively. y z x W U

8. Nomenclature y0.5 Um/2 t ym Um Uj b
Now, we review the nomenclature to help us describe wall jets. <click> Capital U’s are time-averaged flow velocities. The condition at the slot exit is the bulk velocity Uj. At a given x location, Um is the maximum streamwise velocity. <click> Yhalf is the normal distance from the wall where half of Um occurs in the outer flow. This is referred to as the jet half-width, which is traditionally used as the characteristic length scale of the flow.
y0.5
Um/2 t ym Um Uj b

9. Experimental set-up wire mesh Y/b = 19 t/b = 1/9 b x/b = 50 to 208
We constructed a test facility with a slot top thickness of 1/9 of the slot width b. The separation between the bottom to top wall is 19 slot widths. Our velocity measurements are in the developed flow region downstream of the slot exit. The slot top boundary condition is partially open.
t/b = 1/9 b
x/b = 50 to 208

10. Experimental set-up Wire mesh 16 x 16 openings/in2 Dwire = 0.46 mm
open area = 50.7%
The wire mesh had 16 by 16 openings per square inch. The wire diameter was just under half a millimetre. This resulted in an open area of about 50% of the total mesh area.

11. Measurement apparatus
Dantec MiniCTA 54T30 system
sampling frequency = 1 kHz
55P61 x-wire probe
wire diameter = 5 x 10-6 m
wire length = 1.25 x 10-3 m
Calibration
Pitot-static tube + U-tube manometer
Traverse
accuracy = 0.2 x 10-3 m
NI PCI-6071E card
12-bit resolution
Velocities were measured with a hot-wire anemometer with a cross wire probe. The rapid velocity fluctuations in the turbulent flow was sampled at 1 kHz. The hot-wire system was calibrated in-situ with a Pitot static tube and U-tube manometer. The hot-wire probe was positioned with a traverse system with an accuracy of 0.2 mm. Analog to digital conversion of the output voltage signal was done with a National Instruments card. The hot-wire signals were acquired with a PC.

12. Uncertainty analysis Propagation-of-uncertainties approach
(Wheeler & Ganji 1996)
U = f(A, B, C, …)
An uncertainty analysis was done following the approach given in Wheeler and Ganji. The basic idea is that knowing velocity as a function of some variables, we can estimate the velocity uncertainty from the uncertainties of those variables. We evaluate the partial derivatives of the function with respect the variables, and multiply these with the respective uncertainties of the variables. Then we combine everything as a root-sum-square for a total uncertainty estimate on U.

13. Uncertainty analysis Sources of uncertainty considered:
Random variation of the measurand
Ambient temperature variations during measurements
Potential x-wire probe misalignment (≤ 2°)
Potential pitot-static tube misalignment (≤ 2°)
A/D conversion uncertainties
Scale readability limitation of the calibration manometer
Calibration curve-fitting
X-wire probe yaw coefficient uncertainties
The sources of uncertainty considered in the analysis are as listed. Over most of the velocity range, the dominant sources are the ones in pink. At the low end of the velocity range, curve-fitting of the calibration data is the main contributor.

14. Uncertainty analysis
The uncertainty of the velocity measurement varies with the magnitude of velocity being measured. The analysis confirmed that lower velocity measurements have higher uncertainty. Overall, we can say that the uncertainty of our velocity measurements is ±8.4% or less.

15. Plane wall jet velocity profiles
So now we’ll look at some results from our plane wall jet facility. The mean velocity profiles in the developed region of the flow showed agreement with other results in the literature. There weren’t any surprises there, so those results will be shown later in the comparison with radial wall jet mean profiles. The turbulence intensity profiles were a bit more interesting. This graph plots streamwise turbulence intensity against distance from the wall. Our measurements at 50 and 150 slot widths downstream of the slot exit are shown with squares and diamonds, respectively. Maximum local turbulence intensity increases from 19% to 25% with increasing streamwise distance. Wygnanski and his collaborators used a similar slot top thickness and show profiles for a smaller but comparable fetch. Plotted with x’s, their data seems consistent with ours. Since the normalized profiles at varying x/b do not collapse onto one curve, we say there is no similarity for the turbulence profiles. For a free shear layer, normalized turbulence profiles do exhibit similarity. Recalling that the time-averaged velocity profile of the outer layer of the wall jet resembles a free shear layer, we’d expect at least the outer range of the turbulence profiles to show evidence of similarity. This is not evident for the thin slot top data.

16. Plane wall jet velocity profiles
To the preceding plot, we add the solid line from Abrahamsson and collaborators. Their profiles for x/b = 70 to 150 collapsed onto this single curve. Eriksson and collaborators also show data that collapses reasonably well about Abrahamsson’s curve. What did they do differently from Wygnanski and our experiment?

17. Plane wall jet velocity profiles
Slot exit Reynolds number is lower for Eriksson and Abrahamsson than the present study and Wygnanski, but they are all within an order of magnitude. There are prominent differences in the slot top thickness and top boundary height for Eriksson and Abrahamsson compared to the present study and Wygnanski. t/b and Y/b for Eriksson and Abrahamsson only vary by 1. This is the fully closed slot top condition, whereas we have a thin slot lip condition. The application we were developing our facility for required minimal t/b and maximum Y/b, so we have yet to look at the effect of varying these parameters. It would be interesting to increase t/b in our facility and check for collapse of turbulence profiles. Also, increasing Y/b to the value Eriksson used may have an effect on the turbulence profile similarity.

18. Plane wall jet development
Jet spread x0
x/b=0
In addition to velocity profiles, the jet spread and velocity decay are used to characterize the wall jet development. The jet spread relation indicates how the half-width varies with streamwise location. The velocity decay relation indicates how the local maximum velocity varies with streamwise location. We are interested in the constants A and B, and the exponents m and n. xo is the virtual origin. If the jet is considered as being emitted from a source upstream of the slot exit, the virtual origin is this distance upstream of the slot exit. Unfortunately, xo is not documented very well in the literature. However, for the developed region of the jet, x is orders of magnitude larger than xo, so its plausible that the effect of xo is small.
m =1
(14 of 16 experiments)

19. Velocity profile comparison
Our plane wall jet results are shown with the square and diamond. This experimental data shows a reasonable match with Verhoff’s empirical relation, which is the red line. From all the data we examined, Verhoff’s relation is representative of the plane wall jet profile of time-averaged velocity. Although there is not as much data available for the radial wall jet, Wood and collaborators provide a relation that is valid at radial distances greater or equal to 1.5 nozzle diameters. This is plotted in thick black. The radial wall jet profile shows a slight shift away from the wall when compared to the plane wall jet profile. Otherwise, they match surprisingly well. Hot-wire data from Knowles and Myszko for the radial wall jet is plotted with their stated uncertainty of ±2%. Uncertainty bars for the plane wall jet are omitted on this graph for clarity of presentation, but it appears that the difference between plane are radial wall jet profiles is less than experimental uncertainty.

20. Velocity profile comparison
Plane wall jet (Verhoff 1970)
The two solid curves on the preceding graph can be described mathematically. The plane and radial wall jet profiles take the same mathematical form. We have a term raised to a power and a term involving the error function. The power term dominates in the wall jet inner layer, yielding a boundary-layer type flow near the wall. The error function term dominates in the wall jet outer layer, yielding a free shear type flow above the velocity maximum.
Radial wall jet (Wood et al. 2001)

21. Velocity profile comparison
Knowles and Myszko show that radial wall jet streamwise turbulence intensity profiles collapse at radial distances greater than 4.5 nozzle diameters. However the best agreement of magnitude with plane wall jet profiles is before the radial profiles are fully developed. The radial profile plotted in red is at a radius of 2 nozzle diameters.

22. Jet spread comparison Plane wall jet Radial wall jet
Looking at the m and n exponent parameters from the literature, radial and plane wall jets both appear to spread linearly in most studies. Comparing the arithmetic mean of slope for each type of wall jet, the radial wall jet spreads at a slightly greater rate. This may be due to the greater entrainment of ambient air in radial wall jets.

23. Conclusions
turbulence profile similarity dependency on slot top geometry
profiles of time-averaged velocity for plane and radial wall jets match within experimental error
linear spread rate of plane wall jet
= 0.83 linear spread rate of radial wall jet
For the plane wall jet, time-averaged streamwise velocity profiles collapse when normalized by the jet half-width. However, similarity of turbulence profiles normalized by the half-width appears to depend on the slot top geometry.
Correlation analysis indicated no linear relationship between the spread and decay parameters and each of the facility geometry parameters (t/b, Y/b, Z/b). A marginal linear relationship was observed between slot Reynolds number and the velocity decay parameters. From comparison of profiles of the time-averaged velocity for plane and radial wall jets, we see that they match within experimental error. Turbulence intensity profiles in the developing region of the radial wall jet have comparable shape and magnitude to the profiles in the developed region of the plane wall jet. Finally, we see that the linear spread rate of the plane wall jet is 83% of the linear spread rate of the radial wall jet.

24. Future work
turbulence profile similarity dependency on slot top geometry
investigation of the Reb dependency of the velocity decay parameters
measurements in large plane wall jet facility (2.5 m x 2 m cross-section)
Future work includes investigating the effect of the slot top geometry on the turbulence profile similarity and the effect of slot Reynolds number on the velocity decay parameters.

25. Acknowledgements Sponsors: UWO University Machine Shop C. Novacco
Dr. G.A. Kopp and Dr. R.J. Martinuzzi
This work would not have been possible without the financial support of our sponsors. The UWO University Machine Shop fabricated parts for the experimental facility. C. Novacco spent a summer helping us with data acquisition and post-processing. Some test equipment was kindly made available by Profs. Kopp and Martinuzzi. The AFM Group provided encouragement.