Abstract
An annular jet proximity sensor sometimes exhibits instabilities if it is not well designed. In the previous paper, we indicated that the instabilities are caused by the negative resistance in the output characteristics of the sensor. In this paper, the output characteristics are analytically derived. In the analysis, a two-dimensional flow model is used to simplify the analysis instead of an annular jet model, and the theory for two-dimensional reattaching jet flow by Bourque & Newman is modified and applied. As a consequence, it is analytically shown that the negative resistance appears in the two-dimensional model, and that the cause of negative resistance is explained as follows.
Since the main jet deflects outward with increasing the output flow, the reflected jet flow returned into a cavity decreases, and, moreover, the average dynamic pressure of the reflected jet which impinges on the output port decreases. Consequently, the rise of output pressure affected by the dynamic pressure of the reflected jet reduces with increasing the output flow. This is the cause of negative resistance. On the other, hand, the cavity pressure as well as the resistance at the output port generates a positive resistance in the output characteristics. The negative resistance is apt to appear in the neighborhood of zero output flow, because the resistance of output port is small in that region. The experimental results with two-dimensional models are found to be in qualitative agreement with the theoretical results.
