Frequency Response Model for Branched Pneumatic Sensing Systems

A frequency response model for branched pneumatic sensors is developed. A typical application is prediction of pneumatic latency and attenuation in aircraft airdata systems, where pneumatic lines are branched to feed a variety of instruments, navigation systems, and pilot displays. The model is developed using small perturbations of the unsteady Navier-Stokes equations. The linearized equations are radially averaged and expressed in the frequency domain. The result is one-dimensional boundary value problem where the pressure oscillation for a given frequency is expressed as a function of position within the sensor. Assuming constant tube geometry and gas properties along an arbitrarily small tubing element allows a closed-form solution of the boundary value equations. This solution becomes a fundamental building block for solving the frequency response of more complex pneumatic geometries. The analysis process employed is similar to applying Kirchhoff's laws to analyze complex electrical circuits. The model predictions are compared against experimental data generated for a simple two-branch configuration. Comparisons for both symmetrical and unbalanced branches are presented. Experiment setup and procedures are described. The comparisons show that the model accurately predicts both the magnitude and phase frequency response of dominant and reflected wave harmonics within each branch of the system.