cases:case034

Plane Mixing Layer

The subsonic turbulent plane mixing layer under investigation has the following characteristics: external velocities of $U_a = 42.8$ and $U_b = 25.2$ m/s, fully turbulent co-flowing boundary layers; the test section is $30\times 30$ cm2. Measurements are made both upstream and downstream of the location where the mixing layer should reach an asymptotic, self-similar, state.

Flow Characteristics

The ML (mixing layer) is created by a flat plate splitting two air streams ($U_a = 42.8$m/s and $U_b = 25.2$m/s; $r = U_b/U_a = 0.6$), as shown in figure 1. The co-ordinates are $X$ in the streamwise direction, $Z$ parallel to the trailing edge and $Y$ normal to the $XZ$ plane ($Y = 0$ at centre line of the ML).

Fig. 1: Flow geometry and configuration

The use of a long splitter plate, with sandpaper strips towards its upstream end, allowed the boundary layers to be fully turbulent by the trailing edge of the plate. The table below summarizes their features.

Quantities measured at $X=-10$ mm Notation High velocity side boundary layer Low velocity side boundary layer
Velocity $U_{\infty}$ 41.54 m/s 22.40 m/s
Thickness (99%) $\delta$ 9.6 mm 6.3 mm
Displacement thickness $\delta_1$ 1.4 mm 1.0 mm
Momentum thickness $\theta$ 1.0 mm 0.73 mm
Shape factor $H$ 1.35 1.37
Momentum Reynolds number $Re_{\theta}$ 2900 1200
Turbulence level $u'/U_{\infty}$ $\approx 0.3%$ $\approx 0.3%$

Profiles of mean and rms streamwise velocity just downstream of the splitter plate are available in 0001-ml1.dat.

Experimental Apparatus and Data Processing

This experimental investigation of the plane mixing layer is based on a 12 X hot-wires rake in the mean-gradient direction ($Y$). Special HW rakes have been designed. A Printed Circuit Board (PCB) and miniature probes fully located inside the PCB are used. The probes have a $1\times 1$ mm2 square section with 0.2mm diameter prongs. Wires are 0.5mm long with a 2.5µm diameter. For holding each probe, a $1\times 1$mm2 groove is machined on the PCB surface. Both X or single probes may be used within the same rake. Velocity can simultaneously be sampled at up to 100 kHz for each of the 24 channels.

The separation between probes is 6mm and the rake extent is about twice the local vorticity thickness $\delta_w$. By comparing spectra, space time correlations and higher order moments with the corresponding results obtained with conventional one or two single probes, it has been shown that the Hot-Wire-Rake (HWR) does not significantly perturb the flow, at least for the above mentioned characteristics.

Measurements using the X-wire probes have been carried out both in the asymptotic part of the ML (at $X=650$, $800$ and $950$ mm), where the mean flow and turbulence profiles are expected to be self-similar and the vorticity thickness to grow linearly, as well as further upstream (at $X=150$, $200$ and $250$ mm).

Single hot-wire data have also been obtained at a number of locations, and comparisons of profiles from the two systems show very close agreement.

Data available includes:

• Development of mixing layer width, and momentum thickness along the channel
• Profiles of mean velocity, Reynolds stresses and triple moments at selected streamwise locations
• Budgets of $U$ momentum, $k$ and $\overline{uv}$ at $X=200$ and $800$ mm
• Pdf and spectra at selected locations.

Sample plots of selected quantities are available.

The files in the tables and links below are profiles and quantities most likely to be used in making comparisons between simulations, for example. The full set of data, from which these have been extracted, and which also contains pdf and spectra data, as well as some further explanatory notes, is available as shl04-files.tar.gz.

File Data Contained
0001-ml1.dat Profiles of mean and rms streamwise velocity just downstream of the splitter plate
delom-ml1.dat Development of vorticity thickness, $\delta_{\omega}$, along the channel
theta-ml1.dat Development of momentum thickness, $\theta$ along the channel

First, second and third order velocity moments:

Streamwise location Mean velocities Reynolds stresses Triple moments
$X=150$ mm 0150-m1.dat 0150-m2.dat 0150-m3.dat
$X=200$ mm 0200-m1.dat 0200-m2.dat 0200-m3.dat
$X=250$ mm 0250-m1.dat 0250-m2.dat 0250-m3.dat
$X=650$ mm 0650-m1.dat 0650-m2.dat 0650-m3.dat
$X=800$ mm 0800-m1.dat 0800-m2.dat 0800-m3.dat
$X=950$ mm 0950-m1.dat 0950-m2.dat 0950-m3.dat
File Data Contained
kuv-200.dat $k$ and $\overline{uv}$ profiles at $X=150$, $200$ and $250$ mm
kuv-800.dat $k$ and $\overline{uv}$ profiles at $X=650$, $800$ and $950$ mm
eps-200.dat Dissipation rate profile at $X=200$ mm
eps-800.dat Dissipation rate profile at $X=800$ mm

Budget data:

File Data Contained
budg-momentum-200.dat Budget terms from the $U$ momentum equation at $X=200$ mm
budg-momentum-800.dat Budget terms from the $U$ momentum equation at $X=800$ mm
budg-balancuv-200.dat Budget terms from the $\overline{uv}$ equation at $X=200$ mm
budg-balancuv-800.dat Budget terms from the $\overline{uv}$ equation at $X=800$ mm
budg-prodk-200.dat Terms appearing in the $k$ generation at $X=200$ mm
budg-prodk-800.dat Terms appearing in the $k$ generation at $X=800$ mm
budg-convk-200.dat Terms appearing in the $k$ convection at $X=200$ mm
budg-convk-800.dat Terms appearing in the $k$ convection at $X=800$ mm
budg-diffk-200.dat Terms appearing in the $k$ diffusion at $X=200$ mm
budg-diffk-800.dat Terms appearing in the $k$ diffusion at $X=800$ mm
budg-eps-200.dat Dissipation rate of $k$ at $X=200$ mm
budg-eps-800.dat Dissipation rate of $k$ at $X=800$ mm
1. Delville, J., Bellin, S., Garem, J.H., Bonnet, J.P. (1989). Analysis of structures in a turbulent, plane mixing layer use of a pseudo flow visualization method based on hot-wire anemometry. Advances in Turbulence 2, Eds. H.H. Fernhols, H.E. Fiedler, Springer Verlag.

Indexed data:

case034 (dbcase, free_flow)
case034
titlePlane Mixing Layer
authorDelville, Bellin, Garem, Bonnet
year1989
typeEXP
flow_tag2d, mixing_layer