Plane Mixing Layer
Experiments by Delville, Bellin, Garem, Bonnet
Description
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.
Experimental Details
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.
Available Measurements
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 data can be downloaded as compressed archives from the links below, or as individual files.
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 |
References
- 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) | |
|---|---|
| case | 034 |
| title | Plane Mixing Layer |
| author | Delville, Bellin, Garem, Bonnet |
| year | 1989 |
| type | EXP |
| flow_tag | 2d, mixing_layer |