======Flat Plate Transitional Boundary Layers======
=====Experiments by Coupland=====

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====Description====

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.

<imgcaption cas20-geom| Experimental setup and details of test plate>{{ figs:case020:test20c.gif | Experimental setup}}</imgcaption>

===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 {{cdata:case020:t3ccp.dat|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 Details====

===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 <imgref cas20-geom>. 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 <sup>o</sup>C 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 20<sup>o</sup>C). 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.

====Available Measurements====

For each of the eight cases, there are four data files:
  - A summary of the development of boundary layer integral parameters etc.
  - Profiles from single wire data at a number of \(x\) locations
  - Profiles from U-V cross wire data at a number of \(x\) locations
  - Profiles from U-W cross wire data at a number of \(x\) locations

[[case020-plots|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:

  * {{cdata:case020:fptr-allfiles.tar.gz|fptr-allfiles.tar.gz}}
  * {{cdata:case020:fptr-allfiles.zip|fptr-allfiles.zip}}

^ Case   ^  Summary  ^  Single wire data  ^  U-V cross wire data  ^  U-W cross wire data  ^
| T3A-   |  {{cdata:case020:t3amy.dat|t3amy.dat}}  |  {{cdata:case020:t3ams.dat|t3ams.dat}}  |  {{cdata:case020:t3amv.dat|t3amv.dat}}  |  {{cdata:case020:t3amw.dat|t3amw.dat}}  |
| T3A    |  {{cdata:case020:t3ay.dat|t3ay.dat}}  |  {{cdata:case020:t3as.dat|t3as.dat}}  |  {{cdata:case020:t3av.dat|t3av.dat}}  |  {{cdata:case020:t3aw.dat|t3aw.dat}}  |
| T3B    |  {{cdata:case020:t3by.dat|t3by.dat}}  |  {{cdata:case020:t3bs.dat|t3bs.dat}}  |  {{cdata:case020:t3bv.dat|t3bv.dat}}  |  {{cdata:case020:t3bw.dat|t3bw.dat}}  |
| T3C1   |  {{cdata:case020:t3c1y.dat|t3c1y.dat}}  |  {{cdata:case020:t3c1s.dat|t3c1s.dat}}  |  {{cdata:case020:t3c1v.dat|t3c1v.dat}}  |  {{cdata:case020:t3c1w.dat|t3c1w.dat}}  |
| T3C2   |  {{cdata:case020:t3c2y.dat|t3c2y.dat}}  |  {{cdata:case020:t3c2s.dat|t3c2s.dat}}  |  {{cdata:case020:t3c2v.dat|t3c2v.dat}}  |  {{cdata:case020:t3c2w.dat|t3c2w.dat}}  |
| T3C3   |  {{cdata:case020:t3c3y.dat|t3c3y.dat}}  |  {{cdata:case020:t3c3s.dat|t3c3s.dat}}  |  {{cdata:case020:t3c3v.dat|t3c3v.dat}}  |  {{cdata:case020:t3c3w.dat|t3c3w.dat}}  |
| T3C4   |  {{cdata:case020:t3c4y.dat|t3c4y.dat}}  |  {{cdata:case020:t3c4s.dat|t3c4s.dat}}  |  {{cdata:case020:t3c4v.dat|t3c4v.dat}}  |  {{cdata:case020:t3c4w.dat|t3c4w.dat}}  |
| T3C5   |  {{cdata:case020:t3c5y.dat|t3c5y.dat}}  |  {{cdata:case020:t3c5s.dat|t3c5s.dat}}  |  {{cdata:case020:t3c5v.dat|t3c5v.dat}}  |  {{cdata:case020:t3c5w.dat|t3c5w.dat}}  |

A text file {{cdata:case020:readme.txt|readme.txt}} has further explanations and details of
the file naming etc.


====References====

  - 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.).
  - Ryhming, I. (1990). Testcase Specifications. In //Numerical simulation of unsteady flows and transition to turbulence//, (eds. Pironneau, D. , Rode, W., Ryhming, I.L.).
  - ERCOFTAC Special Interest Group on Laminar to Turbulent Transition & Retransition. T3D Test case problem obtained from University of Thessaloniki.
  - Savill, A.M. (1993). [[https://doi.org/10.1007/BF01082590|Evaluating turbulence model predictions of transition]]. //Appl. Sci. Res.//, Vol. 51, pp. 555-562.

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Indexed data:
<data dbcase semi_confined_flow>
case       : 020
title      : Flat Plate Transitional Boundary Layers
author*    : Coupland
year       : 1990
type       : EXP
flow_tag*  : 2d, transition, 2dbl
</data>