An Adaptive Response Compensation Technique for the Constant-Current Hot-Wire Anemometer ()
1. Introduction
In recent years, particle image velocimetry (PIV) has become one of the most popular techniques for measuring velocity fields. The hot-wire anemometry [1-5], on the other hand, has long been used mainly for measuring turbulent gaseous flows because of its simple and highlyreliable measurement systems and wide range of applicability. Thus, the hot-wire anemometry is still frequently utilized as a reliable research tool for statistical and frequency analyses of turbulent flows.
The hot-wire anemometry is generally driven at three operation modes, i.e., the constant temperature, constantcurrent and constant voltage modes. For the application of the hot-wire anemometry, the constant-temperature anemometer (CTA) is commercially available and almost always used as a standard system for driving the hot-wire, while the other two modes are rarely used, primarily due to their response lag during velocity fluctuation measurement. However, the electric circuit of the CTA is not simple, and the measurement system is fairly expensive. On the other hand, the constant-current hot-wire anemometer (CCA) can be set up with a very simple and low-cost electric circuit for heating the hot-wire. Thus, if we improve the response characteristics of the CCA with the aid of digital signal processing, the CCA will have a great advantage over the CTA and will be a promising tool for multipoint turbulence measurement.
When a hot-wire is driven at a constant electric current, the wire temperature, which corresponds to the hot-wire output, does not respond correctly to high-frequency velocity fluctuations because of the thermal inertia of the wire. Thus, the CCA output needs to be compensated adequately for the response lag to reproduce high frequency components of the measurement data. In order to investigate the response characteristics of the hot-wire, Hinze [1] analyzed the dynamic behavior of the hot-wire with heat loss to the wire supports. As a result, it was shown that the aspect ratio of the hot-wire (the lengthto-diameter ratio) is an important parameter characterizing the response of the hot-wire. In our previous studies [6,7], we have successfully derived a precise theoretical solution for the frequency response of an actually-used hot-wire probe which consisted of a fine metal wire, stub parts (copper-plated ends/silver cladding of a Wollaston wire) and prongs (wire supports). As a result, we were able to find the geometrical conditions for the frequency response of the CCA to be approximated by the firstorder lag system, which can be characterized by a single system parameter called the thermal time-constant [5].
If the time-constant value is known in advance, we may apply the existing response compensation techniques for the first-order system [4,5] to recover the response delay in the CCA measurement. In reality, however, since the time-constant value of the CCA changes largely depending on flow velocity [8] and physical properties of the working fluid, it is very difficult to estimate the time-constant value of the hot-wire accurately. In our previous papers [6,7], we proposed a digital response compensation scheme based on the precise theoretical expression for the frequency response of the CCA. The results showed that the scheme worked successfully, reproducing high-frequency velocity fluctuations of a turbulent flow. However, this compensation scheme needs more information regarding the geometrical parameters of the hot-wire probe, i.e., the diameters and lengths of the wire and stub together with their physical properties.
In the present study, first, we thoroughly tested the theoretical expression for the frequency response of the CCA by applying it extensively to the digital response compensation of three different hot-wire probes consisting of tungsten wires 5 μm, 10 μm and 20 μm in diameter. Secondly, we have proposed a novel approach to the response compensation of the CCA output that will work without our knowing in advance the geometrical parameters of the hot-wire probe. This approach is based on a two-sensor probe technique for compensating the response delay of fine-wire thermocouples [9,10], and enables in-situ estimation of the time-constant values of the hot-wire probe, and will realize adaptive response compensation of the CCA outputs. Specifically, in the twosensor probe technique, two hot-wires of unequal diameters—having different response speeds—are used simultaneously, and the time-constant values of the two hotwires can be obtained from the measurement data itself without carrying out any dynamic calibration of the hotwire probe.
Finally, in order to demonstrate the usefulness of the CCA, we have applied the above response compensation schemes to multipoint velocity measurement of turbulent flows e.g., [11-13]. In the present multipoint measurement, we have simultaneously used 16 hot-wires driven by the CCA to measure a turbulent wake flow formed behind a cylinder. In these verification experiments, we have measured turbulence intensities (r.m.s. values), power spectra and instantaneous signal traces of the velocity fluctuations, and have compared them with those obtained by a hot-wire probe driven by a commercially available constant-temperature hot-wire anemometer.
2. Time Constant of Hot-Wire for CCA Mode
Figure 1 shows the geometrical features and coordinate system of the CCA probe used in the theoretical analysis (see Appendix A). As shown in Figure 1, the hot-wire is a fine tungsten wire (sensing part) with copper-plated ends (stubs) which are soldered to the prongs (wire supports). By applying electric current I to the fine-wire element (length: dx, diameter d1), the generated Joule heat should balance with the sum of the following heat losses: heat convection, heat conduction, heat accumulation and thermal radiation. Since the heated wire is very fine, we can assume that the amount of heat radiation is negligible and the cross-sectional temperature distribution is uniform [14]. Therefore, the energy balance equation for the hot-wire can be written as (in this section, the subscript 1 for wire or 2 for stub is omitted for simplicity):