An integrated 3D sound intensity sensor using four-wire particle velocity sensors: II. Modelling

The sensitivity of a micromachined acoustic sensor consisting of four hot-wire particle velocity sensors is analysed theoretically and experimentally. The device and its fabrication have been presented in part 1 of this paper (Yntema et al 2010 J. Micromech. Microeng. 20 015042). A relatively straightforward analytical model is presented that describes both the air flow around the probe and the temperature profile around the heated wires. The presence of the chip surface near the heated wires influences the fluid flow around the wires, while it also affects the temperature distribution in the probe by altering the direction of heat transport. Both effects result into a modified angular dependence of the sensor sensitivity with respect to the normal 'figure-of-eight' figure of the response. By means of finite elements software, the thermal and the acoustic flow behaviour of the sensor are also investigated numerically, both effects together and each apart, and the results are compared to the analytical model. Comparison with the experimental data is presented, showing that the model is appropriate to describe the angular dependence and the magnitude of the sensor response. It is concluded that the perturbed air flow due to the chip surface is the dominant reason for the observed angular sensitivity.