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

Abstract

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.

Comparing the adiabatic and isothermal pressure dependence of the index of refraction in a drop-weight apparatus

“…Although it occurs only after the pressure pulse is over, there are lingering effects of turbulence and persistent gas bubbles, particularly in sebacate. One could imagine that the shape of a subsequent pressure pulse might be affected by this mixed state of the fluid if the waiting time is too short [26]. We have found that one needs to wait Fig.…”

“…A look through the optical windows can serve as a partial quality control. For best results, de-gassed fluids should be used [26].…”

“…The second frame was taken 0.467 ms after the first, the next 1.367 ms later, and the last one another 6.425 ms later a minute or more for the visible perturbations to clear away. One could envision that there might be bubbles permanently getting stuck in the small ducts leading to the piezoelectric pressure sensors, potentially changing their effective response [26]. This might need to be taken into account for devices that calibrate a pressure sensor by comparison to a second, reference sensor.…”

Dynamic measuring methods: a review

“…The necessity for the dynamic measurement of pressure arises at low [65] and high [66] temperatures of gases and liquids [67].…”

Nonlinear model of a servo-hydraulic shaking table with dynamic model of effective bulk modulus

“…In recent years, several theoretical models have been proposed to simulate the dependency of the E-Modulus upon pressure and entrained air content [22,23,24,25,26]. In [27,28], based on the experimental verification of these models, have been shown that the IFAS model in [24] can simulate the behavior of the E-Modulus with higher accuracy. However, as shown in these papers, the minimum time for maximizing the input pressure are 2.5[s], which in our study is almost the steady state case.…”