Frequency Response of Guard-Heated Hot-Film Wall Shear Stress Sensors for Turbulent Flows

Guard-heated thermal sensors were recently proposed for the measurement of wall shear stress (or ‘‘skin friction’’) fluctuations in turbulent flow, to overcome the severe errors due to substrate heat conduction encountered in conventional single-element (SE) hot-film sensors. An earlier computational study of steady-state performance showed that a sensor with guard-heating in two-planes (GH2P) can eliminate errors due to spatial averaging and axial heat conduction in the fluid, both of which limit the spatial resolution of conventional SE sensors. Here we present analytical and numerical results comparing the dynamic behavior – frequency response and phase lag – of the guard-heated and conventional designs.

For the water–glass fluid-substrate combination, sensor amplitude and phase errors begin only at a frequency near the onset of attenuation due to boundary layer thermal inertia. In this case, although the SE sensor suffers spatial averaging errors, it shows low amplitude attenuation and phase lag, close to that of the GH2P sensors, up to fc.

For air-glass, analysis suggests and numerical results confirm, that the response of the conventional SE sensor is dominated by unwanted substrate heat transfer, with rapid signal attenuation beginning at frequencies that are five orders of magnitude smaller than fc. In this case, guard-heating enables strong improvement in the dynamic response, with a small drop in the amplitude response ratio from 0.95 to 0.85 (compared to 0.95 to 0.06 for the SE sensor) and negligible phase lag errors over an additional five decades of frequency. For the guard-heated design, upstream pre-heating occurs, but does not use heat drawn from the sensing element. Numerical results show that signal phase lag is zero and amplitude deviations are small, with modest variation over four decades of frequency. Guard-heated (GH2P) sensors appear to be an attractive option for wall shear stress fluctuation measurement in turbulent flows. 

Analyzing Guard-Heating to Enable Accurate Hot-Film Wall Shear Stress Measurements for Turbulent Flows

In this paper we examine guard-heated hot-film sensors for the measurement of wall shear stress fluctuations in turbulent flows, using analytical and numerical techniques. The new thermal sensor designs proposed here, seek to eliminate the most severe source of error in conventional single-element hot-film sensors – which is indirect heat transfer to the fluid flow through the solid substrate. Published studies of the single-element hot-film show that a significant portion of the heat generated in the hot-film travels through the substrate before reaching the fluid, which causes spectral and phase errors in the wall shear stress signal and can drastically reduce the spatial resolution of the sensor. In addition, heat conduction parallel to the surface, within the fluid near the sensor edges, can produce significant errors when sensors are made smaller to improve spatial resolution. Here we examine the effectiveness of forcing zero tem- perature gradient at the edges of the hot-film in eliminating these errors. Air and water flow over such guard-heated sensors are studied numerically to investigate performance and signal strength of the guard-heated sensors. Our results show, particularly for low-conductivity fluids such as air, that edge guard-heating needs to be supplemented by a sub-surface guard-heater. With this two-plane guard-heat- ing, a strong non-linearity in the standard single-element designs can be corrected, and substrate conduc- tion errors contributing to spectral distortion and phase errors can be eliminated.