Liquid-circular Angular Accelerometer Research Articles

MSD-based transient fluid model of liquid circular angular accelerometer for vibration-induced error analysis

This paper investigates the errors induced by linear vibration in the fluidic system of liquid circular angular accelerometers (LCAAs). A two-dimensional mass-spring-damper model is proposed to analyze the pressure difference between both sides of LCAA transducer subjected to linear vibration in both transient and steady states, where the compressibility of fluid is taken into account. The complex flow patterns of fluid are simplified to the positional changes of fluid particles. Springs and dampers are utilized to simulate the forces inside the fluid and between the fluid and the tube wall. Simulations are carried out based on the linear acceleration step excitation to explore the influence of model parameters, LCAA structure parameters and fluid parameters. The proposed model is validated by comparing the characteristics of the simulated pressure difference with their corresponding theoretical values, and is further verified by the comparison with the results from computational fluid dynamics method. Furthermore, the pressure difference under linear acceleration excitations in various forms is analyzed. The results indicate that the abrupt changes in linear acceleration are the primary cause of pressure difference oscillation, and the compressibility of fluid leads to increased pressure difference.

Electrokinetic coupling in unsteady pressure-driven flow through a porous transducer: Fractal capillary bundle model

• A fractal capillary bundle model is used to predict the frequency-dependent streaming potential coefficient of porous media. • The theoretical model of electrokinetic coupling in the unsteady pressure-driven flow is established to characterize the frequency response of the streaming potential coefficient. • An analytic solution of Poisson-Boltzmann equation is obtained for the capillary bundle of porous media with high zeta potential condition. • The proposed model shows satisfactory agreement with experiments and can optimize the parameter configuration of transducers. The liquid circular angular accelerometer (LCAA) is a novel fluid-mechanical device based on the principle of electrokinetic effect, which is featured as the streaming potential coefficient (SPC) to convert elastic wave energy into electromagnet energy within the porous transducer. To determine its dynamic response, we present an analytical expression for the frequency-dependent SPC of a porous transducer in the LCAA. The electrokinetic coupling process in unsteady pressure-driven flow is developed by using the fractal capillary bundle model. Electrical potential distribution in a torturous capillary of the arbitrary radius is modeled by a modified approximation for the Poisson-Boltzmann equation with high zeta potential condition. We present an apparatus for measuring the dynamic SPC of transducers that are sintered with glass beads and have high porosity. Measurements on natural and sintered porous samples validate the proposed model and demonstrate satisfactory agreement. According to the sensitivity analysis, changes in fluid and structural properties have a significant impact on the unsteady SPC response, particularly the solution concentration and mean particle size. The findings of this study can pave the way for the frequency-dependent SPC prediction of the porous transducer as well as a better understanding of the LCAA design optimization.

Frequency-Dependent Streaming Potential in a Porous Transducer-Based Angular Accelerometer.

This paper presents a transient model of streaming potential generated when fluid flows through a porous transducer, which is sintered by glass microspheres and embedded in the circular tube of a liquid circular angular accelerometer (LCAA). The streaming potential coupling coefficient (SPC) is used to characterize this proposed transient model by combining a capillary bundle model of a porous transducer with a modified Packard’s model. The modified Packard’s model is developed with the consideration of surface conductance. The frequency-dependent streaming potential is investigated to analyze the effect of structure parameters of porous media and the properties of the fluid, including particle size distribution, zeta potential, surface conductance, pH, and solution conductivity. The results show that the diameter of microspheres not only affects bandwidth and transient response, but also influences the low-frequency gain. In addition, the properties of the fluid can influence the low-frequency gain. Experiments are actualized to measure the steady-state value of permeability and SPC for seven types of porous transducers. Experimental results possess high consistency, which verify that the proposed model can be utilized to optimize the transient and steady-state performance of the system effectively.

Permeability Model for Porous Transducer With Glass Spheres Packing

A theoretical model is developed for predicting permeability of a porous transducer, which is a crucial component of liquid circular angular accelerometer and sintered by glass microspheres. The proposed permeability model of the transducer is determined with consideration of its shape factor, tortuosity, and particle size distribution (PSD) characterized by equivalent mean diameter and skewness. A novel analytical method for calculating the shape factor for the arbitrary cross-section area is derived. In addition, a tortuosity model is designed by fitting skewness and tortuosity of particle packing beds in a regular tetrahedron microspheres arrangement structure. Together with the analytical model of shape factor, the tortuosity fitting model and a method to determine equivalent diameter from PSD, the permeability model is implemented to compare with Kozeny–Carman (KC) model. The experiments are performed to measure the permeability of four types of porous transducers fabricated with different PSDs and consequently validate the permeability model. The results indicate that the proposed model can be utilized for predicting permeability of porous transducer with higher precision.

The influence of tube wall on fluid flow, permeability and streaming potential in porous transducer for liquid circular angular accelerometers

The effects of the tube wall on the fluid flow, permeability and streaming potential are reported for a porous transducer for use in a liquid circular angular accelerometer. Fluid flow and pressure near the surface of the transducer are modeled and validated numerically. We show that the differential pressure across the transducer is not affected by the tube wall. A capillary bundle model is employed to represent the transducer to obtain the radial porosity, permeability and streaming potential distributions due to wall effects. A simulated spherical packing is generated from measured particle parameters to specify the model by calculating the radial porosity distribution. The theoretical permeability and streaming potential coupling coefficient are located within one standard deviation from the mean of measurements. Due to the radial distribution of streaming potential, the electrode can be configured into a large streaming potential region to measure the signal more efficiently. Three electrode configurations are described based on these results, which can be applied to increase the signal of the sensor.

Permeability modeling for porous transducer of liquid-circular angular accelerometer

This paper is concerned with the permeability modeling for a kind of porous transducer, which is sintered by glass microspheres. This kind of transducer is used to measure the streaming potential in the liquid-circular angular accelerometer. Kozeny-Carman (KC) equation is improved by taking into account the shape of fluid channel, the porosity of porous transducer, and the particle size distribution (PSD) of glass microspheres in the transducer. Under the assumption of star-like fluid channels, the shape factor is analyzed numerically and further evaluated. The notion of equivalent diameter of microspheres is applied to avoid the error of permeability calculation resulting from the usage of the average diameter. By implementing the experiments of transducers with 9 different PSDs, a relationship among the equivalent diameter, the tortuosity, the average diameter, the porosity and the skewness of the PSD is obtained. The comparison results illustrate that the proposed permeability model considerably reduces the large prediction errors of the previous models when dealing with the mixture of different microspheres and the large skewness of PSD.

Modeling for Fluid Transients in Liquid-Circular Angular Accelerometer

Liquid-circular angular accelerometer is generally designed with the circular tube, the fluid mass, and the porous transducer. With the consideration of the fluid compressibility, a novel theoretical model of the fluidic system of this sensor is developed based on the theory of fluid transients for the first time. Simulation and experiments are conducted to prove the validity of the proposed model and the model manifests satisfactory performance to calculate the natural frequency, the resonances, the bandwidth, and the low-frequency gain of the fluidic system. Moreover, the influences of several structure parameters are analyzed by using the proposed model. The wave speed in the fluid mass affects the bandwidth of the fluidic system grossly, while the radius of the circular tube has effects on both the gain and the bandwidth. Besides, the liquid resistance of the transducer and the cross-sectional area of the circular tube are found to exert analogous influences on the frequency response of the fluidic system.