======Airfoil Boundary Layer and Wake======
=====Experiments by Nakayama=====

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====Description====

Flows around two different airfoil models: a conventional one at zero
incidence and a supercritical one at an angle of attack of 4<sup>o</sup>, in the same
flow conditions. 2D flows at low Mach number.


===Geometry of the Computational Domain===

The two wing shapes are shown in <imgref cas11-geom>.

Chord of both airfoils: \(C = 24\) in. \(\approx 610\) mm.

<imgcaption cas11-geom| Airfoil geometries>{{ figs:case011:test11.gif | Airfoil geometries}}</imgcaption>

Features of the two models:

|   ^  Model A  ^  Model B  ^
^ Airfoil  |  10%-thick conventional  |  14%-thick advanced supercritical  |
^ Including angle at trailing edge   |  10.18<sup>o</sup>  |  10.05<sup>o</sup>  |
^ Angle of attack  |  0<sup>o</sup>  |  4<sup>o</sup>  |
^ Trailing-edge thickness (mm)  |   0.6  |  0.018  |

The coordinates of the airfoil surfaces are stored in the files {{cdata:case011:model_a_cor.dat|model_a_cor.dat}} and {{cdata:case011:model_b_cor.dat| model_b_cor.dat}}. There appear to be errors in a few of the data points provided in these files, which if used would lead to kinks in the airfoil geometries. If computing these cases it might be best to disregard such points, or smooth over them.


===Flow Characteristics===

The variations of the total and the static pressures are less than 1% in the flow direction along the wind tunnel.

The boundary layers are made turbulent for both models: 
  * on the upper surface, using a wire of diameter 1.3 mm located at \(x/C=0.16\)
  * on the lower surface, using a wire of diameter 0.5 mm located at \(x/C=0.05\)

The experimental results indicate that the flow around the conventional airfoil is a minor perturbation of 
a symmetric flat-plate flow with small wake curvature and weak viscous-inviscid interaction. The flow 
around the supercritical airfoil is in considerable contrast, with strong streamwise pressure gradients, 
non-negligible normal pressure gradients and large surface and streamline curvatures of the trailing-edge 
flow. In this case, the near-wake is strongly curved and intense mixing occurs between the retarded 
boundary layer of the upper-surface and the strongly accelerated one of the lower-surface.

===Flow Parameters===

  * Air at standard conditions.
  * Reference freestream velocity: \(U_{ref} = 30.5\) m/s.
  * Reynolds number based on the chord length: \(Re_C = 1.2\times 10^6\).

==Inflow Conditions==

The upstream flow is reported to be at a constant velocity \(U_{ref} = 30.5\) m/s,
with a freestream turbulence level of 0.02%.
 
====Experimental Details====

  * Surface pressure measurements using a standard static pressure probe. The pressure coefficient is defined as \(C_p = (p - p_{ref})/(0.5\rho U_{ref}^2)\) where \(p_{ref}\) is the undisturbed freestream pressure far upstream from the airfoil.
  * Total pressure measurements using a flattened tube both in the boundary layer and in the immediate vicinity of the trailing edge. A circular tube is used for the rest of the wake.
  * Shear stress measurements using L-shaped Preston tubes.
  * Velocity measurements using a hot-wire.

===Measurement Errors===

| \(\delta(C_p)\) | \(\pm 0.03\)  |
| \(\delta(\text{second order moments})\) |  5% of the maximum value  |

====Available Measurements====

The data can be downloaded as compressed archives from the links
below, or as individual files.

  * {{cdata:case011:airf-allfiles.zip|airf-allfiles.zip}}
  * {{cdata:case011:airf-allfiles.tar.gz|airf-allfiles.tar.gz}}

[[case011-plots|Sample plots]] of selected quantities are available.

The following measurements are provided for the two models.

  * Velocity measurements: Profiles at selected locations across the upper and the lower side boundary layers and across the wake of:
       * First order moments: \(U/U_{ref}\), \(V/U_{ref}\)
       * Second order moments: \(\overline{u^2}/U_{ref}^2\), \(\overline{v^2}/U_{ref}^2\), \(\overline{uv}/U_{ref}^2\)
       * Third order moments (at some locations): \(\overline{uuu}/U_{ref}^3\), \(\overline{vvv}/U_{ref}^3\), \(\overline{uuv}/U_{ref}^3\), \(\overline{uvv}/U_{ref}^3\)
  * Pressure measurements
      * Distribution of the wall pressure and friction coefficients around the two models.
      * Contour maps of the pressure coefficient around the trailing edge.

Data is stored in the following files:

^   ^  Model A  ^  Model B  ^
^ Airfoil coordinates    |  {{cdata:case011:model_a_cor.dat|model_a_cor.dat}}  | {{cdata:case011:model_b_cor.dat|model_b_cor.dat}}  |
^ Surface pressure data  |  {{cdata:case011:model_a_sfd.dat|model_a_sfd.dat}}  | {{cdata:case011:model_b_sfd.dat|model_b_sfd.dat}}  |
^ Hot wire data          |  {{cdata:case011:model_a_hwd.dat|model_a_hwd.dat}}  | {{cdata:case011:model_b_hwd.dat|model_b_hwd.dat}}  |
^ Pitot tube data        |  {{cdata:case011:model_a_ptd.dat|model_a_ptd.dat}}  | {{cdata:case011:model_b_ptd.dat|model_b_ptd.dat}}  |
^ Station data           |  {{cdata:case011:model_a_std.dat|model_a_std.dat}}  | {{cdata:case011:model_b_std.dat|model_b_std.dat}}  |


====Main References====

  - Nakayama, A. (1985). [[https://doi.org/10.1017/S0022112085003433|Characteristics of the flow around conventional and supercritical airfoils]]. //J. Fluid Mech.//, Vol. 160, pp. 155-179.

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Indexed data:
<data dbcase flow_around_body free_flow>
case       : 011
title      : Airfoil Boundary Layer and Wake
author*    : Nakayama
year       : 1983
type       : EXP
flow_tag*  : 2d, wake, streamlined_body
</data>