In temperature measurement of non-isothermal fluid flows by a contact-type temperature sensor, heat conduction along the sensor body can cause significant measurement error which is called “heat-conduction error.” The conventional formula for estimating the heat-conduction error was derived under the condition that the fluid temperature to be measured is uniform. Thus, if we apply the conventional formula to a thermal field with temperature gradient, the heat-conduction error will be underestimated. In the present study, we have newly introduced a universal physical model of a temperature-measurement system to estimate accurately the heat-conduction error even if a temperature gradient exists in non-isothermal fluid flows. Accordingly, we have been able to successfully derive a widely applicable estimation and/or evaluation formula of the heat-conduction error. Then, we have verified experimentally the effectiveness of the proposed formula using the two non-isothermal fields—a wake flow formed behind a heated cylinder and a candle flame—whose fluid-dynamical characteristics should be quite different. As a result, it is confirmed that the proposed formula can represent accurately the experimental behaviors of the heat-conduction error which cannot be explained appropriately by the existing formula. In addition, we have analyzed theoretically the effects of the heat-conduction error on the fluctuating temperature measurement of a non-isothermal unsteady fluid flow to derive the frequency response of the temperature sensor to be used. The analysis result shows that the heat-conduction error in temperature-fluctuation measurement appears only in a low-frequency range. Therefore, if the power-spectrum distribution of temperature fluctuations to be measured is sufficiently away from the low-frequency range, the heat-conduction error has virtually no effect on the temperature-fluctuation measurements even by the temperature sensor accompanying the heat-conduction error in the mean-temperature measurements.

Topics
Candle flame, Thermoelectricity, Thermal conductivity, Thermal instruments, Thermodynamic states and processes, Physical radiation effects, Transition metals, Catalysts and Catalysis, Combustion, Fluid flows
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The compensation procedure based on the frequency response function is explained in detail in our previous paper.16 The outline is as follows: (1) apply the fast-Fourier-transform (FFT) to the sensor output (time-series data); (2) multiply the FFT output by the inverse of the response function, i.e., H−1(ω), and (3) apply the inverse FFT to the frequency-domain data thus obtained.
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2013
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