Dynamic Response Modeling and Calibration of Pitot Probes with Enhanced Spatial Resolution

Knowledge of the dynamic response characteristics of a pressure sensor is essential for accurate extraction and analysis of fluctuating components within a flowfield. In hypersonic flows, second-mode disturbance growth (100 kHz to 300 kHz) is a dominant boundary-layer instability that drives laminar-turbulent transition for certain geometries. These second-mode fluctuations occur within the millimeters-thick boundary layers, imposing a spatial resolution challenge for high-frequency commercial pressure sensors that are a few millimeters in diameter. Forward-mounted hypodermic tubing creates a line-cavity system with sufficient spatial resolution to reconstruct a hypersonic boundary layer. These hypodermic tubes induce resonant peaks and amplitude attenuation in the measured spectra. These tubing effects must be compensated for to obtain the true fluctuation characteristics of the measured boundary layer. Analytical computations for the system response of line-cavity geometries were calculated using the Bergh-Tijdeman formula. MATLAB codes were written to perform these recursive calculations for the original and alternate versions such as the Kutin-Svete formulation. Calculations of single-, double-, and triple-tube systems were presented to show the effect of varying tube or cavity dimensions. For single-tube systems, it was shown that average resonant-peak spacing is determined by tube length, but resonant peak frequencies could be shifted by changing tube diameter, cavity dimensions, mean temperature, or mean density. Using a shock tube, the dynamic response of a Kulite line-cavity system was measured. Tubing geometry with inner diameters ranging from 0.05 mm to 1.75 mm and lengths from 4.75 mm to 12.7 mm were used to vary the system geometry. Spectra from the transient step-response data were calculated using the Gans-Nahman method. Measured frequency responses were compared to analytic solutions, showing strong agreement of primary resonance peak frequency and amplitude for tube diameters of 0.84 mm and larger. Tube diameters below 0.25 mm had system responses that dropped below unity gain earlier and had weaker resonance amplification than analytical predictions. The effectiveness and issues of various system identification procedures are discussed. The frequency responses of the Kulite line-cavity systems are used to estimate biproper transfer functions H(s). These models are used to recover the untubed Kulite time- and frequency-domain responses. The compensated signals have R^2 > 0.9 over the frequencies used to model H(s). Directions for performing this model estimation and compensation using MATLAB are provided. Although these data were acquired with resolution that was found to be too low to detect second-mode waves, the procedure to extend the compensation range and overcome many associated limitations has been demonstrated.