The simplest case is represented by the vector of the averaged velocity, which lies in the XY plane, while V and W equal zero. Let U, V, and W be the relevant components of the velocity vector in the system of X, Y, Z coordinates ( Figure 1) and their pulsation components be u, v, and w. The hot-wire anemometer, besides measuring a mean velocity, is an efficient instrument for diagnostics of turbulence characteristics, viz., intensities of temperature and velocity component fluctuations, coefficients of turbulent transfer of momentum and heat, spatial and temporal scales, etc. Which has been verified experimentally at 1/D > 600. The gauge thermal balance can be represented as
Contemporary instrument circuits afford, at an optimal alignment, a bandwidth up to 100 kHz.
The instantaneous disbalance voltage of the bridge determines an instantaneous value of velocity pulsation. In the constant- temperature hot-wire anemometer a feedback amplifier controls the bridge current so as not to upset the bridge balance and, consequently, to retain the gauge resistance and temperature constant and independent of the cooling rate. The gauge is connected by a shielded coaxial cable to one of the arms of Wheatstone bridge, the opposite arm being connected to a variable resistance controlling the overheat factor m = R w/R f (see Figure 2). One or the other regime is used depending on the specific character of measurements. The hot-wire anemometer operates in two regimes, viz., a constant-current regime (I w = const) when the gauge voltage pulsations are attributable to temperature variation and, hence, the wire resistance, and the regime of constant temperature (T w = const), maintained by the feedback system with a variable current heating the sensor. Measurement of voltage drop across the wire allows, if the physical properties of the gauge material and the mechanism of heat transfer are known, the determination of local fluid velocity. Measuring the velocity in gases is carried out with (T w - T f) typically in the range 180 to 200 K and in water, from 20 to 40 K. The gauge sensitivity to the flow velocity is provided by having the wire or film temperature T w substantially higher than the flow temperature T f, which is achieved by heating it by electric current. In film gauges a 1 to 5 μm thick film is deposited on a cone-, wedge-, or cylinder-shaped substrate for measuring velocity or on a plane substrate for measuring shear stresses on the wall. The wire is welded or soldered to stainless steel prongs with a diameter at the tips of 0.1 to 0.2 mm. Usually the gauge wire is between 1 to 10 μm in diameter D and from 0.5 to 2 mm in length 1. In these materials, resistance to a good accuracy depends linearly on temperature R w = R 0 (1 + α rgr T w), where R 0 is the wire resistance at T = 0☌ and T w is the wire transfer (0☌). Figure 1. Sensor of hot wire anemometers.
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