cases:case064

# Flow Approaching a Wall-Mounted Cylinder

The data is from experiments that were carried out in a three-dimensional incompressible turbulent boundary layer growing in front of a cylinder standing on a flat wall in a wind tunnel (see figure 1).

Beginning with the quasi two-dimensional boundary layer far in front of the cylinder, the development of the boundary layer profiles were investigated along a streamline of the free stream up to the region behind the “three-dimensional” separation. At 14 different stations, profiles were measured of the mean velocity vector, the 6 components of the turbulent stress tensor, the static pressure and in addition the wall shear stress vector. The turbulence measurements were carried out with a single hot wire probe and with a rotatable X-probe, whose axis could be aligned with the direction of the local mean velocity. From this data the direction of the velocity gradient and of the turbulent shear stress were evaluated.

Fig. 1: Flow configuration and experimental setup

#### Description of the Working Section

The measurements were carried out in the boundary layer wind tunnel of the Institut für Strömungslehre und Strömungsmaschinen of the University of Karlsruhe. figure 1 shows a sketch of the working section which is a rectangular duct of 1500 mm × 300 mm cross section and 3000 mm length. The cylinder diameter is 320 mm with a streamlined afterbody which prevents separation.

The cylindrical body extends from the floor to the roof, the working area being near to the floor. The boundary layer probes are mounted in a probe-holder which is movable normal to the walls and can be rotated around the axis normal to the walls by a traversing mechanism. The probe-holder fits through slots in the upper wall of the working section and can be shifted together with the traversing gear along the slots whose direction is parallel to the tunnel axis. In addition, a part of the roof plate is movable spanwise together with the probe. The floor plate is designed in a similar manner with pressure taps and the possibility of inserting flush-mounted hot films. This design of the working section allows every point of the working area to be reached by the probes.

In addition to the direction of the streamlines in the free stream the magnitude of the velocity and the static pressure were also measured, as was the static pressure at the wall.

One streamline in the free stream was chosen. along which the boundary layer profiles were investigated at 10 separate stations (No. 1 - 10). In addition, 2 stations (No. 11 and 12) on a streamline further removed from the cylinder and 2 Stations (No.13 and 14) on the median plane were chosen (see figure 2).

At these 14 stations the following variables were measured:

• the vector of the mean velocity
• the 6 components of the Reynolds stress tensor
• the static pressure
• the value and direction of the wall shear stress

For presentation purposes a streamline co-ordinate system is used for the velocity components in the data files whose $x$-axis is aligned with the direction of the mean velocity at the edge of the boundary layer and projected onto the wall at every station.

Fig. 2: Locations of measurement stations

#### Experimental Methods

In the free stream area the value of the mean velocity $U$ was measured with a Pitot-tube and a static pressure probe after evaluation of its direction with a Conrad-tube. Inside the boundary layer the value of the mean velocity vector $U_s$, the yaw angle $\gamma$ and the turbulence intensity $\sqrt{\overline{u_s^2}}$ were measured with a boundary layer type single hot-wire sensor with gold plated ends.

The pitch angle $\beta$ and the remaining 5 components of the stress tensor were measured with a X-probe. The design of the probe holder allowed yawing around the $y$-axis, pitching relative to the wall and turning around the probe axis without the probe tip leaving the measurement point. It was thus possible to align the probe axis with the local direction of the mean velocity $U_s$. Due to this alignment the two wires of the X-probe are equally sensitive to the fluctuating component in the direction of the local mean velocity and to the component normal to the mean velocity which lies in the plane formed by the wire and the mean velocity. By turning the X-probe around its axis in steps of 45 degrees, combined with suitable processing of the signals, the 6 components of the Reynolds stress tensor can be evaluated.

The static pressure inside the boundary layer was evaluated with the usual disc-probe; pressure taps were used for the wall pressure. The value of the wall shear stress was measured with a Preston-tube. The direction of the wall streamlines was evaluated in 3 different ways:

• from the oil flow pattern
• by extrapolating the direction of the mean velocity at a wall distance $y = 0.2$ mm
• with a turnable flush-mounted hot-film probe

Measurements available include profiles of mean velocities and Reynolds stress components, together with flow yaw and pitch angles, at 14 locations, as indicated in figure 2 and in the table below.

Sample plots of selected quantities are available.

 Pressure gradients in $x$ (streamwise) and $z$ (cross-stream) directions decfel-cp.dat
Profiles of Mean Velocities and Reynolds Stresses
Location File
Station No. $x$ [mm] $z$ [mm]
1 0 75 decfel1.dat
2 200 77.5 decfel2.dat
3 350 82 decfel3.dat
4 425 87 decfel4.dat
5 475 93 decfel5.dat
6 501 97 decfel6.dat
7 526 102 decfel7.dat
8 551 108.5 decfel8.dat
9 563 112.5 decfel9.dat
10 575 117 decfel10.dat
11 601 234 decfel11.dat
12 676 252.5 decfel12.dat
13 0 0 decfel13.dat
14 425 0 decfel14.dat
1. Dechow, R., Felsch, K.O. (1977). Measurements of the mean velocity and of the Reynolds stress tensor in a three-dimensional turbulent boundary layer induced by a cylinder standing on a flat wall. Proc. Int. Symp. on Turbulent Shear Flows, University Park, PA.

Indexed data:

case064 (dbcase, semi_confined_flow)
case064
titleFlow approaching a wall-mounted circular cylinder
authorDechow, Felsch
year1977
typeEXP
flow_tag3d, surface_mounted_body