Experimental Facility and Measurement Technique

The tests were performed in the Princeton University 3 x 4 ft smoke tunnel. A sketch of the tunnel is shown in Fig. 2.1 and also on the back cover. It consists of an inlet and stilling chamber 9 ft high by 12 ft wide containing screens and flow straighteners. The flow straighteners are 3 in square and 12 in long. This section is followed by a 9:1 contraction leading to the test section which is 3 ft high by 4 ft wide. Downstream of the test section the flow is turned 90° and exits through a 50 HP fan. The tunnel speed in the test section is variable from 5 to 70 ft/s.

2.1 Flow Quality

Constant temperature hot-wire anemometry5 (using Dantec model 55M01) was used to determine turbulence levels in the freestream. At all conditions the wire was operated at an overheat of 0.8. The frequency response was optimized using the standard test in which a square wave in voltage is injected at the Wheatstone bridge to simulate an impulse in velocity. The —3 dB point of the response curve was 33 kHz for chord Reynolds numbers of 100k, 200k, and 300k; and 25 kHz for a Reynolds number of 60k. As will be shown shortly, these frequencies are well above the energy-containing frequencies of the turbulence.

A common problem when measuring turbulence levels in low-speed facilities is determining the lowest frequency of interest. Usually, the anemometer signal is high-pass filtered. This procedure reduces the apparent RMS turbulence level by removing low-frequency fluctuations which may be important to boundary layer transition. In this work, however, no high-pass filter was used. Instead, the DC component (the mean) of the anemometer signal was subtracted (“bucked off”) using an operational amplifier of an analog computer. The remaining signal was then amplified to fill the ±10 volt range of the 14-bit analog-to-digital converter and sampled at frequencies from 10 Hz to 10 kHz. By sampling over a range of frequencies, high resolution of the spectra was obtained. In each case the low- pass frequency of the filter was set to somewhat less than the Nyquist sampling frequency to eliminate aliasing errors. A sampling frequency of 100 Hz resolved the high-frequency end of the spectrum and extended down to sufficiently low frequencies.

All spectra presented here were found using a sampling frequency of 100 Hz with the hot wire located 3 in below the center of the tunnel. This location was representative of the turbulence characteristics throughout the central region of the test section. For each run, 9216 points were taken and then broken into ensembles of 1024 to calculate spectra. Spectra at several different Reynolds numbers are shown in Figs. 2.2 (а-d). Power spectral density multiplied by fre­quency is plotted against the logarithm of frequency. In this way, the area under the curve is directly proportional to («rme)2/^oo—the square of the turbulence intensity. As can be clearly seen, the majority of the energy is found at frequen­cies below 1 Hz. If the signal were high-passed at 1 Hz, this contribution to the turbulence would be lost. Perhaps fluctuations at frequencies this low have quasi-steady effects; in any event it is currently unclear what cut-off frequency should be used so both numbers are presented. The unfiltered turbulence levels at various Reynolds numbers are given below. Note that these levels correspond to a very low cut-off frequency of 0.01 Hz due to the sampling interval. Turbu­lence levels are also indicated below for the case of a cut-off frequency of 1 Hz.

Mean-pressure surveys to determine the uniformity of the freestream were taken in the test section throughout a plane perpendicular to the flow. Less than 4% variation was found in the static pressure and there was no measurable total pressure variation. These surveys indicate a 2% variation in the velocity which was deemed sufficiently uniform.