 Constant-temperature hot-wire anemometer

A constant-temperature hot-wire anemometer is a hot-wire anemometer whose electrical feedback adjusts wire heating to keep a chosen wire resistance approximately constant. The resistance acts as a temperature indicator; increasing flow cooling calls for increased electrical power. The primary manufacturer's arrangement places the wire in a Wheatstone bridge controlled by a servo amplifier.^[ref]

A simple resistance-temperature calibration illustrates the setpoint. If the cold resistance at fluid temperature $T_a$ is $R_a$, approximateFor stipulated $R_a=5\Omega$, $R_w=7.5\Omega$ and ${\alpha }_R=0.004{\mathrm{K}}^{-1}$, the overtemperature is $125\mathrm{K}$. At ambient $20{}^{\circ }\mathrm{C}$, that corresponds to wire temperature $145{}^{\circ }\mathrm{C}$ in this linear model. These parameters are illustrative, not universal tungsten specifications. A fixed resistance setpoint and a fixed overtemperature require different adjustments when ambient temperature changes.

At steady state, the heating balances convective, support-conduction and radiative losses. The observed bridge output must be calibrated against known flow with the same probe, fluid and operating conditions. A bridge output squared may follow an empirical relation $E^2=A+B{U}^n$ over a limited range, but circuit ratios and losses matter before identifying that output with wire power. The manufacturer's technical account separately treats velocity, directional and temperature calibration.^[ref]

Finite-bandwidth thermal feedback in hot-wire anemometry can be explored with an original local model. Let a temperature perturbation satisfywhere $C_w>0$ is wire heat capacity, $K>0$ a linearized thermal-loss coefficient and $F>0$ the incremental cooling per speed change. An ideal proportional power controller applies $\delta P=-K_c\delta T$, with $K_c>0$. HenceA cooling perturbation first lowers temperature, causing the controller to raise power. Finite feedback gain leaves a residual temperature perturbation and gives DC power sensitivity $F{K}_c/(K+K_c)$.

For $C_w=10^{-8}J/K$, $K=10^{-4}W/K$ and $K_c=9\times 10^{-4}W/K$, the model's thermal time constant changes from $100$ to $10\mu \mathrm{s}$ and its half-power frequency from about $1.59$ to $15.9\mathrm{kHz}$. The closed-loop DC response is $0.9F$. This calculation assumes an instantaneous controller; real amplifier and cable dynamics can add phase lag and limit usable gain.

A proposed characterization calibrates the steady speed response, then applies a small electrical test perturbation and examines settling and ringing while measuring ambient temperature. Check the response over the intended flow range and verify that the measuring electronics do not clip. The primary practical guide describes the feedback bridge as part of the complete measuring chain.^[ref] A fast electrical response alone does not establish spatial resolution or uniquely determine the direction of a reversing flow.