Coriolis-induced instabilities in centrifuge modeling of granular flow

Granular flows are typically studied in laboratory flumes based on common similarity scaling, which create stress fields that only roughly approximate field conditions. The geotechnical centrifuge produces stress conditions that are closer to those observed in the field, but steady conditions can be hardly achieved. Moreover, secondary effects induced by the apparent Coriolis acceleration, which can either dilate or compress the flow, often obscure scaling. This work aims at studying a set of numerical experiments where the effects of the Coriolis acceleration are measured and analyzed. Three flow states are observed: dense, dilute, and unstable. It is found that flows generated under the influence of dilative Coriolis accelerations are likely to become unstable. Nevertheless, a steady dense flow can still be obtained if a large centrifuge is used. A parametric group is proposed to predict the insurgence of instabilities; this parameter can guide experimental designs and could help to avoid damage to the experimental apparatus and model instrumentation. Graphic abstract

The effect of the centrifugal acceleration on period spacings of gravito-inertial modes in intermediate-mass stars

Context. The Kepler and Transiting Exoplanet Survey Satellite (TESS) space telescopes delivered high-precision, long-duration photometric time series for hundreds of main-sequence stars, revealing their numerous gravito-inertial (g) pulsation modes. This high precision allows us to evaluate increasingly detailed theoretical stellar models. Recent theoretical work extended the traditional approximation of rotation, a framework to evaluate the effect of the Coriolis acceleration on g modes, to include the effects of the centrifugal acceleration in the approximation of slightly deformed stars, which so far have mostly been neglected in asteroseismology. This extension of the traditional approximation was conceived by re-deriving the traditional approximation in a centrifugally-deformed, spheroidal coordinate system. Aims. We explore the effect of the centrifugal acceleration on g modes and assess its detectability in space-based photometric observations. Methods. We implemented the new theoretical framework to calculate the centrifugal deformation of pre-computed 1D spherical stellar structure models and computed the corresponding g-mode frequencies, assuming uniform rotation. The framework was evaluated for a grid of stellar structure models covering a relevant parameter space for observed g-mode pulsators. Results. The centrifugal acceleration modifies the effect of the Coriolis acceleration on g modes, narrowing the equatorial band in which they are trapped. Furthermore, the centrifugal acceleration causes the pulsation periods and period spacings of the most common g modes (prograde dipole modes and r modes) to increase with values similar to the observational uncertainties of the measured period spacing values in Kepler and TESS data. Conclusions. The effect of the centrifugal acceleration on g modes is formally detectable in modern space photometry. The implementation of the used theoretical framework in stellar structure and pulsation codes will allow for more precise asteroseismic modelling of centrifugally deformed stars in order to assess its effect on mode excitation, trapping, and damping.

Design of a Coriolis Acceleration Experimental Device

Important drawbacks of Coriolis experimental setup and devices are their multiple parts and cost to own. Simplicity, traceability, and measurability are the major concern. This paper presents a preliminary design process of Coriolis acceleration experimental device to visualize the effect of Coriolis and enable the calculation of acceleration components to facilitate students for a better understanding of this phenomenon. This is realized through a slidable collar with a marker and accelerometer attached on it and a rotating rod that shows a visible yet erasable mark from the marker’s path. The design process went through typical engineering design processes such as morphological study, functional decomposition, and Pugh chart. Next, Finite Element Analyses (FEA) were performed to determine the mode shapes, followed by analytical calculation of the dynamic reaction experienced by motor. In addition, this kit provides opportunity for students to manually calculate the actual acceleration component based on theory learnt which is considered innovative. The use of controllable motor for rotating the rod could vary the travelling path of the marker, subsequently diversify the problems for student to solve.

Analysis and Evaluation of a Coriolis Acceleration Experimental Device

The Coriolis acceleration is the product of linear and rotational velocities. Acceleration analysis is important because inertial forces are proportional to their rectilinear, angular, and Coriolis accelerations. The magnitudes of Coriolis acceleration vary according to the conditions of motions of an object. This paper presents kinematic analyses of a preliminary design of a Coriolis kit. The Coriolis kit consists of a rotating rod and a slidable collar. A motor is used to rotate the rod and accelerometer is attached to the slider for recording the accelerations. The Coriolis effect is visualized through the mark left by the slider during motion. Common analytical expressions of the Coriolis acceleration are derived and calculated using measured values. Results show that the Coriolis kit is capable to visualize and sketch the travelling path of the object in motion.