cases:case020

# Flat Plate Transitional Boundary Layers

Flat-plate transitional 2D boundary layers flows with or without pressure gradient. No temperature variations.

Free-stream velocity and turbulence intensity vary between $U_o = 1.2$ to $19.8$ m/s, and $Tu_o = 0.9$% to $6.6$%, depending on the case.

Fig. 1: Experimental setup and details of test plate

#### Flow Characteristics

The boundary layers begin to develop as laminar, and then undergo transition to turbulence at a certain distance downstream of the leading edge, depending on the free-stream and pressure gradient conditions. Eight cases are provided; three with with zero pressure gradient, and the others with a non-zero free-stream pressure distribution. For these latter five cases the measured $C_p$ variation is given in file t3ccp.dat. The upstream free-stream velocity and turbulence intensity levels for the various cases are summarized in the table below.

Case Upstream velocity [m/s] Upstream turbulence intensity [%] Pressure gradient
T3A 5.4 3.0 Zero
T3B 9.4 6.0 Zero
T3A- 19.8 0.9 Zero
T3C1 5.9 6.6 Variable
T3C2 5.0 3.0 Variable
T3C3 3.7 3.0 Variable
T3C4 1.2 3.0 Variable
T3C5 8.4 3.0 Variable

#### Experimental Methods

The wind tunnel used in the present experiments is of the closed circuit type and is described in detail in Ryhming (1990). Its major elements include a centrifugal fan blowing through a large plenum fitted with turbulence reducing honeycomb gauzes, a small 2-D contraction, leading to a highly versatile working section, and a wide-angle diffuser. The working section is of 2m length, 0.71m width and 0.26m height with full-length perspex sidewalls for good optical access, see figure 1. The bottom wall can be inclined sufficiently to produce a zero pressure gradient on the test surface, which is hung from the ceiling of the working section. High performance flow cleaning filters are employed in the return ducting, together with a water-cooled heat exchanger. As a result of the careful design, the working section free-stream turbulence intensity is O.2+/-O.O5% over the operating velocity range of 0 to 25 m/s, and the air temperature can be controlled to +/-0.1 oC degrees during the course of a day's operation.

Measurements are made on a flat perspex test surface, which is hung from the roof of the working section. The test plate has numerous static pressure tappings and surface plugs, which are interchangeable and flush to within 25µm (when the tunnel is operated at a nominal 20oC). The (1700mm length, 20mm thick, 710mm wide) test surface is extremely flat and employs a small leading edge radius of 0.75mm with a 5 degree chamfer on the other side to the (lower) test-surface. The test plate leading edge is mounted 4Omm from the working section upper wall, and the circulation about it is controlled by a combination of a trailing edge flap and adjusting the pressure drop across the working section exit plane (by means of gauzes). Moreover, the test plate is inclined at 0.5 degree to the main flow vector which, together with the circulation control measures, ensures attached, steady, leading edge flow with the stagnation streamline located on the test surface.

The turbulence generating grids used in these experiments are also detailed in Ryhming (1990), together with the turbulence intensity characteristics. These can be located at the entrance plane of the working section, at the downstream end of the 2-D contraction. They are made of square or round bars and woven wire mesh, and are positioned 610 mm upstream of the test plate leading edge. The grids have been designed to generate test plate free-stream turbulence intensities from 0.5% to 7% and integral length scales from 5mm to 30mm. With the grids in location, it was found that the generated turbulence was extremely homogeneous and isotropic, with streamwise-to-normal fluctuating velocity ratio of about 1.005.

A DISA 55M series anemometer system was used to make velocity measurements in the wind tunnel. Custom designed single and X-wire probes (total wire length 1.5mm, sensing length 0.5mm, wire diameter 2.5µm) were used to measure both the free-stream turbulence properties and the boundary layer velocity profiles. Gold-plated wire probes have been used to minimise prong interference, with the small sensing length chosen to minimise spatial averaging from both the turbulent eddies and from the mean velocity shear. The primary purpose for using the single wire probes is to get sufficiently close to the test surface in order that accurate measurements of the boundary layer integral parameters could be made. In practice, the probe prongs were always placed on the test surface with the traverse proceeding away from this surface, ending at about three times the boundary layer thickness. The minimum wire height was measured to be 29µm but because the wall proximity error was found to be significant (for $y^+ < 3$), a certain number of measured points were deleted from the profiles before analysing the data. The single wire probes also provide an initial estimate of the streamwise component of fluctuating velocities, which may be compared with the X-wire results.

The X-wires (both $U$-$V$ and $U$-$W$ components) were used to measure normal and shear stress distributions through the boundary layers. They provide measurements of all three components of normal stresses, together with two components of shear stress ($\overline{uv}$ and $\overline{uw}$) A number of techniques have been examined to measure surface shear stress. In the case of a turbulent boundary layer, the law of the wall has been used with the Karman and offset constants of 0.41 and 5.20 respectively.

A Preston tube has also been used (making use of Patel's calibration), and comprises a square-cut circular tube of 2.49mm outside diameter, located on the surface of a test surface plug.

The momentum balance approach was also used and it was found that all three techniques yielded skin friction coefficients which agreed to within 2% of each other. Attempts were made at calibrating both a heated film gauge (DISA R45) and a small (50µm height) razor blade device in both turbulent and laminar boundary layers. The aim was to produce a 'universal' calibration which could be used in both laminar and turbulent flows, and by implication in the transitional zone also. Unfortunately, these attempts failed for various reasons. As a result, it was decided to use the momentum balance technique in both the laminar and transitional zones. This was compared with the wall-slope approach in laminar boundary layers with negligible free-stream turbulence and found to agree to better than 1%.

The single wire measurements have been made at typically 15 streamwise locations, and up to 46 points within each boundary layer. Sample times of approximately 30 seconds per measurement have been used, with a bandwidth of 3kHz on-line, and 10kHz recorded.

#### Measurement Error

It should first be noted that corrections have been applied to the data to account for the influence of velocity shear on the UW probe measurements. Even so, the actual magnitude of the results shown will be slightly in error, due to the influence of spatial averaging over the sensor length. It is possible that the single wire measurements of $u'$ are more accurate than those using the cross-probes, the difference becoming greater in proportion to the velocity shear.

For each of the eight cases, there are four data files:

1. A summary of the development of boundary layer integral parameters etc.
2. Profiles from single wire data at a number of $x$ locations
3. Profiles from U-V cross wire data at a number of $x$ locations
4. Profiles from U-W cross wire data at a number of $x$ locations

Sample plots of selected quantities are available.

The files can be downloaded individually, or compressed archives of all data files may be downloaded in the formats:

A text file readme.txt has further explanations and details of the file naming etc.

1. Roach, P.E., Brierley, D.H. (1990). The influence of a turbulent free stream on zero pressure gradient transitional boundary layer development. Part 1: testcases T3A and T3B., In Numerical simulation of unsteady flows and transition to turbulence, (eds. Pironneau, D. , Rode, W., Ryhming, I.L.).
2. Ryhming, I. (1990). Testcase Specifications. In Numerical simulation of unsteady flows and transition to turbulence, (eds. Pironneau, D. , Rode, W., Ryhming, I.L.).
3. ERCOFTAC Special Interest Group on Laminar to Turbulent Transition & Retransition. T3D Test case problem obtained from University of Thessaloniki.
4. Savill, A.M. (1993). Evaluating turbulence model predictions of transition. Appl. Sci. Res., Vol. 51, pp. 555-562.

Indexed data:

case020 (dbcase, semi_confined_flow)
case020
titleFlat Plate Transitional Boundary Layers
authorCoupland
year1990
typeEXP
flow_tag2d, transition, 2dbl