A Study of Bulk Modulus, Entrained Air, and Dynamic Pressure Measurements in Liquids

Accurate static and dynamic pressure measurements in liquids, such as fuel, oil, and hydraulic fluid, are critical to the control and health monitoring of turbomachinery and aerospace systems. This work presents a theoretical and experimental study of the frequency response of pressure transducers and pressure measurement systems in liquid media. First, we theoretically predict the frequency response of pressure transducers based upon a lumped-parameter model. We then present a liquid-based dynamic pressure calibration test apparatus that validates this model by performing several critical measurements. This system first uses a vibrating liquid column to dynamically calibrate and experimentally determine the frequency response of a test pressure transducer, measurement system or geometry. Second, this calibration system experimentally extracts the bulk modulus of the fluid and the percent of entrained and/or dissolved air by volume. Bulk modulus is determined by measuring the speed of sound within the liquid and through static pressure loading while measuring the deflection of the liquid column. Bulk modulus and the entrained/dissolved gas content within the liquid greatly impact the observed frequency response of a pressure transducer or geometry. Gases, such as air, mixed or dissolved into a fluid can add substantial damping to the dynamic response of the fluid measurement system, which makes measurement of the bulk modulus and entrained and/or dissolved air critical for accurate measurement of the frequency response of a system when operating with a liquid media. All experimental results are compared to theoretical predictions.