cases:case067

# Flow along a Streamwise Axially Rotating Cylinder

The data represent the results of an experimental investigation of the three-dimensional turbulent boundary layer formed when an initially collateral boundary layer encounters local transverse motion of the bounding surface The flow field was generated by permitting the collateral boundary layer to develop on the surface of a cylindrical body with an external flow parallel to its axis and with a rotating segment of the cylinder downstream.

Fig. 1: Flow configuration and geometry

Most of the measurements have been obtained at a Reynolds number, based on free-stream axial velocity $U_{\infty}$ and per unit inch, of around 28,800, and a ratio of cylinder surface tangential velocity ($W_s$) to $U_{\infty}$ of 1.45. A few turbulence measurements are available at a higher velocity ratio of 2.2.

#### Experimental Apparatus

The experiment was conducted on the apparatus shown schematically in figure 1. Air, delivered to the rear of the plenum box by a centrifugal blower, was distributed evenly over the 1.4 m (55 in.) square cross section of the plenum by the pressure drop across two layers of 1 inch thick fibreglass air conditioning filters. After passing through three 16-mesh wire screens, spaced 0.38 m (15 in.) apart in the plenum box, the flow entered the annular test section through a contraction of 10.3 area ratio.

The centre-body of the annulus was constructed of 10 in. nominal diameter steel pipe turned to a smooth surface. A hemi-spherical end cap was installed on the front of the centerbody and a strip of sandpaper was glued around the shoulder to stabilise transition of the boundary layer.

The rotating portion of the centre-body was of a drum construction and was machined after it was welded to a 25.4 mm (1 in.) diameter central shaft.

The rotor assembly was dynamically balanced and was supported by rigidly mounted ball bearings in the forward and aft stationary segments of the centre-body. The axial gap between the rotor and the forward portion of the centre-body was maintained at 0.25 mm (0.010 in.) and the radial step between these components was less than 0.025 mm (0.001 in.).

The centre-body assembly was supported from an external angle-iron structure by eight tie rods across the annulus upstream of the test section proper and by two support struts under the rear bearing mount. A pulley was installed on the rear shaft of the rotor, and a V-belt drive, with the belt crossing the air stream downstream of the test section, was powered by an A.C. electric motor mounted beneath the apparatus. Speed variation was accomplished by changing drive pulley sizes.

When assembled and aligned, the rotor was concentric with the stationary portions of the centre-body within 0.019 mm (0.00075 in.) and there was little perceivable vibration when the rotor was turning at its maximum speed. The sheet steel outer wall of the annulus had a slight divergence to eliminate axial pressure gradients due to boundary layer growth.

All of the data were obtained using DISA Model 55F04 and 55F02 hot wire anemometer probes. These probes use tungsten wires with a diameter of 0.0051 mm (0.0002 in.) between wire supports 3 mm apart. The sensing length of the wire is reduced to 1.25 mm by gold plating the wire near the supports. This type of probe was selected primarily to minimise support interference effects. The probes were installed in a traversing mechanism that was mounted on rails over a slot in the outer wall of the test section. A micrometer drive was used to position the probe radially, while the entire mechanism could be rotated about a radial axis with its direction being defined by a protractor disc. To minimise flow interference, the probe support was curved rearward and held the probe with its axis at an inclination of 9 degrees to the wall. An optical device was used to establish the location of the probe relative to the wall at the start of each traverse and was capable of resolution within 0.025 mm (0.001 in.).

#### Measurement Errors

Calibration checks of the hot wire anemometer probes indicated that mean velocity measurements were generally repeatable with +/-1 percent of the free stream velocity.

Similarly, the technique used to define mean flow direction (rotating the wire to the position of minimum signal) was found accurate to +/-1 deg during calibration. When combined with limitations on the accuracy to which the protractor on the traversing mechanism could be read, an error of 1.5 to 2.0 deg in mean flow direction was possible. The potential for errors was considerably higher in the measurements of the turbulence characteristics. Sensitivity studies of the pertinent data reduction equations indicated that errors of 1 deg in the determination of the inclination angle of the wire could produce as much as a 10 percent error in a Reynolds shear stress computed from the data. Other factors, such as variations in the flow direction over the length of the wire and support interference effects, could amplify these errors considerably. Estimates of the error in the definition of the Reynolds stress tensor components $\overline{u^2}$, $\overline{w^2}$, and $\overline{uw}$ indicate they are, in general, accurate on an absolute basis within +/-10 percent.

The techniques employed to define $\overline{v^2}$, $\overline{uv}$ and $\overline{vw}$ were more susceptible to error and the absolute levels of these quantities could be in error by as much as 20 percent. However, much of the data used in the evaluation of these components was obtained in successive traverses with and without surface motion. In these cases, errors arising from such factors as inaccurate definition of the wire inclination introduce a constant bias that, while it influences the absolute results, is not as significant in a relative sense.

Data available includes:

• Profiles of mean velocities $U$ and $W$, rms fluctuating velocities $u'$ and $w'$ and shear stress $\overline{uw}$ at 6 stations ($x=1$, $3$, $5$, $8$, $13$ and $16$ in.)
• Profiles of rms velocity $v'$ and shear stresses $\overline{uv}$ and $\overline{vw}$ at $x=3$, $8$ and $16$ in.

Sample plots of selected quantities are available.

The file readme.txt summarizes the nomenclature used in the data files.

1. Lohmann, R.P. (1976). The response of a developed turbulent boundary layer to local transverse surface motion. Journal of Fluid Engineering, Vol. 98, pp. 354-363.

Indexed data:

case067 (dbcase, semi_confined_flow)
case067
titleFlow along a streamwise axially rotating cylinder
authorLohmann
year1976
typeEXP
flow_tagaxisymmetric, 3dbl