Experimental investigation of the effects of length-to-diameter ratio of hot-wire sensor on the dynamic response to velocity fluctuations

Abstract

This paper reconsidered the criterion on the length-to-diameter ratio (l/d) of the hot-wire sensor, $l/d \ge 200$, for end-conduction effects on the dynamic response of constant-temperature hot-wire anemometer (CTA) to be neglected. Experiments were first conducted using a low-noise compact CTA with hot-wire sensors of l/d = 80, 120, 150 and 200 in a two-dimensional (2-D) circular cylinder wake at a Reynolds number Re = 77, at which a 2-D von Kármán vortex street developed, allowing us to exclude spatial filtering and tangential velocity effects. The damping coefficient in the CTA bridge was tuned to 0.70 for all sensors to reduce possible influences of over- or under-damping on measurements in a frequency range up to 6 kHz. The stubs and prongs of probes consisted of identical materials and dimensions so that the thermal properties were considered to be identical for all probes. Careful comparisons of the amplitudes of the fundamental (1.9 kHz) and higher harmonic components of time-periodic wake vortices showed that the attenuation due to the end-conduction effect in the absence of the spatial filtering and damping coefficient effects was at most 2.5% in terms of the rms value of velocity fluctuations even for l/d = 80. The similar weak attenuation (about 2.6% for l/d = 80) was also observed in the measurements of low-frequency free-stream turbulence. In addition, effects of l/d on the yaw angle response of the sensor were examined in the free stream, revealing that the yaw angle ($\psi$) variation of the measured velocity (both the mean and fluctuations) obeyed the cosine law for $\psi \le 60^\circ$. The Champagne constant k was 0.12 for l/d = 200 and 0.2 even for l/d = 80 in the mean velocity measurement using the present probe with long stubs. On the other hand, the intensity of free stream turbulence measured using a $45^\circ$-yawed sensor was significantly affected by the sensor’s l/d; the rms value of velocity fluctuation was attenuated by about 7.5% for l/d = 80.