scholarly journals Experimental study of the flows in a non-axisymmetric ellipsoid under precession

2021 ◽  
Vol 932 ◽  
Author(s):  
Fabian Burmann ◽  
Jérõme Noir
Keyword(s):  
Tilt Angle ◽  
Rotation Axis ◽  
Theoretical Models ◽  
Base Flow ◽  
Hysteresis Cycle ◽  
Triaxial Ellipsoid ◽  
Axisymmetric Cavity ◽  
Vorticity Component ◽  
Good Agreement ◽  
Total Fluid

Precession driven flows are of great interest for both, industrial and geophysical applications. While cylindrical, spherical and spheroidal geometries have been investigated in great detail, the numerically and theoretically more challenging case of a non-axisymmetric cavity has received less attention. We report experimental results on the flows in a precessing triaxial ellipsoid, with a focus on the base flow of uniform vorticity, which we show to be in good agreement with existing theoretical models. As predicted, the uniform vorticity component exhibits two branches of solutions leading to a hysteresis cycle as a function of the Poincaré number. The first branch is observed at low forcing and characterized by large amplitude of the total fluid rotation and a moderate tilt angle of the fluid rotation axis. In contrast, the second branch displays only a moderate fluid rotation and a large tilt angle of the fluid rotation axis, which tends to align with the precession axis. In addition, we observe the occurrence of parametric instabilities early in the first branch, which saturate in the second branch, where we observe the same order of the kinetic energy in the base flow and instabilities.

Experimental investigation of precession driven flows in a triaxial ellipsoid

2021 ◽  
Author(s):  
Fabian Burmann ◽  
Jerome Noir
Keyword(s):  
Boundary Layer ◽  
Industrial Applications ◽  
Base Flow ◽  
Analytical Models ◽  
Triaxial Ellipsoid ◽  
Core Dynamics ◽  
Boundary Deformation ◽  
Container Shape ◽  
Anomalous Dissipation ◽  
Good Agreement

<p>Precession driven flows are relevant for geo- and astrophysical fluid dynamics as well as industrial applications. In the context of planetary core dynamics, they are attributed to the generation of magnetic fields and/or anomalous dissipation. While precession driven flows have been frequently studied in a cylindrical, spherical or spheroidal container shape, the geometry of a triaxial ellipsoid, representing the geophysical case of core mantle boundary deformation in a tidally locked planet, has received less attention.</p><p>Here, we present results from an experimental study in a triaxial ellipsoid. The main focus of our study is on the base flow of uniform vorticity and we report a good agreement between experimental data and existing semi-analytical models. The amplitude of the time averaged uniform vorticity displays a hysteresis loop as a function of the precession forcing and we demonstrate that this observation depends on the ellipticity of the container. Our study also comprises experiments where the boundary layer is expected to be in a turbulent state. Therefore, we discuss the applicability of an effective damping coefficient in the semi-analytical models to account for the dissipation in a turbulent boundary layer. </p>

Stability and collapse of holes in liquid layers

2018 ◽  
Vol 855 ◽  
pp. 1130-1155 ◽  
Author(s):  
Cunjing Lv ◽  
Michael Eigenbrod ◽  
Steffen Hardt
Keyword(s):  
Liquid Film ◽  
Power Laws ◽  
Theoretical Models ◽  
Liquid Volume ◽  
Capillary Length ◽  
Minimum Thickness ◽  
The Stability ◽  
Film Profile ◽  
Hole Closure ◽  
Good Agreement

We investigate experimentally and theoretically the stability and collapse of holes in liquid layers on bounded substrates with various wettabilities. It is shown that for a liquid layer with a thickness of the order of the capillary length, a stable hole exists when the hole diameter is bigger than a critical value $d_{c}$. Consequently, a further increase of the liquid volume causes the hole to collapse. It is found that$d_{c}$increases with the size of the container, but its dependence on the contact angle is very weak. The experimental results are compared with theory, and good agreement is obtained. Moreover, we present investigations of the dynamics of the hole and the evolution of the liquid film profile after the collapse. The diameter of the hole during collapse and the minimum thickness of the liquid film shortly after the collapse obey different power laws with time. Simple theoretical models are developed which indicate that the collapse of the hole is triggered by surface tension and the subsequent closure process results from inertia, whereas the growth of the liquid column after hole closure results from the balance between the capillary force and inertia. Corresponding scaling coefficients are determined.

scholarly journals The spin-up of a linearly stratified fluid in a sliced, circular cylinder

2016 ◽  
Vol 806 ◽  
pp. 254-303
Author(s):  
R. J. Munro ◽  
M. R. Foster
Keyword(s):  
Circular Cylinder ◽  
Rossby Waves ◽  
Rotation Axis ◽  
A Priori ◽  
Propagation Speed ◽  
Stratified Fluid ◽  
Decay Rates ◽  
The Waves ◽  
Western Half ◽  
Good Agreement

A linearly stratified fluid contained in a circular cylinder with a linearly sloped base, whose axis is aligned with the rotation axis, is spun-up from a rotation rate $\unicode[STIX]{x1D6FA}-\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}$ to $\unicode[STIX]{x1D6FA}$ (with $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FA}\ll \unicode[STIX]{x1D6FA}$) by Rossby waves propagating across the container. Experimental results presented here, however, show that if the Burger number $S$ is not small, then that spin-up looks quite different from that reported by Pedlosky & Greenspan (J. Fluid Mech., vol. 27, 1967, pp. 291–304) for $S=0$. That is particularly so if the Burger number is large, since the Rossby waves are then confined to a region of height $S^{-1/2}$ above the sloped base. Axial vortices, ubiquitous features even at tiny Rossby numbers of spin-up in containers with vertical corners (see van Heijst et al.Phys. Fluids A, vol. 2, 1990, pp. 150–159 and Munro & Foster Phys. Fluids, vol. 26, 2014, 026603, for example), are less prominent here, forming at locations that are not obvious a priori, but in the ‘western half’ of the container only, and confined to the bottom $S^{-1/2}$ region. Both decay rates from friction at top and bottom walls and the propagation speed of the waves are found to increase with $S$ as well. An asymptotic theory for Rossby numbers that are not too large shows good agreement with many features seen in the experiments. The full frequency spectrum and decay rates for these waves are discussed, again for large $S$, and vertical vortices are found to occur only for Rossby numbers comparable to $E^{1/2}$, where $E$ is the Ekman number. Symmetry anomalies in the observations are determined by analysis to be due to second-order corrections to the lower-wall boundary condition.

Two-proton radioactivity within Coulomb and proximity potential model

2021 ◽  
Author(s):  
De-Xing Zhu ◽  
Hong-Ming Liu ◽  
Yang-Yang Xu ◽  
You-Tian Zou ◽  
Xi-Jun Wu ◽  
...  
Keyword(s):  
Potential Model ◽  
Liquid Drop ◽  
Theoretical Models ◽  
Parent Nucleus ◽  
Drip Line ◽  
Liquid Drop Model ◽  
Empirical Formulas ◽  
Proximity Potential ◽  
Proton Radioactivity ◽  
Good Agreement

Abstract In the present work, considering the preformation probability of the emitted two protons in the parent nucleus, we extend the Coulomb and proximity potential model (CPPM) to systematically study two-proton (2p) radioactivity half-lives of the nuclei close to proton drip line, while the proximity potential is chosen as Prox.81 proposed by Blocki et al. in 1981. Furthermore, we apply this model to predict the half-lives of possible 2p radioactive candidates whose 2p radioactivity is energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2016. The predicted results are in good agreement with those from other theoretical models and empirical formulas, namely the effective liquid drop model (ELDM), generalized liquid drop model (GLDM), Gamow-like model, Sreeja formula and Liu formula.

scholarly journals Rotational Effects on Reynolds Stresses in the Solar Convection Zone

1991 ◽  
Vol 130 ◽  
pp. 98-100
Author(s):  
P. Pulkkinen ◽  
I. Tuominen ◽  
A. Brandenburg ◽  
Å. Nordlund ◽  
R.F. Stein
Keyword(s):  
Reynolds Stress ◽  
Convection Zone ◽  
Rotation Axis ◽  
Three Dimensional ◽  
External Parameter ◽  
Reynolds Stresses ◽  
Solar Convection Zone ◽  
Hydrodynamic Simulations ◽  
Solar Convection ◽  
Good Agreement

AbstractThree-dimensional hydrodynamic simulations are carried out in a rectangular box. The angle between gravity and rotation axis is kept as an external parameter in order to study the latitude-dependence of convection. Special attention is given to the horizontal Reynolds stress and the ∧-effect (Rüdiger, 1989). The results of the simulations are compared with observations and theory and a good agreement is found.

scholarly journals Apsidal motion in evolved binary systems

1984 ◽  
Vol 105 ◽  
pp. 419-420
Author(s):  
Alvaro Giménez
Keyword(s):  
Preliminary Report ◽  
Binary Systems ◽  
Main Sequence ◽  
Review Paper ◽  
Theoretical Models ◽  
Eclipsing Binaries ◽  
Apsidal Motion ◽  
Different Sources ◽  
Obvious Extension ◽  
Good Agreement

The study of apsidal motions in eclipsing binaries has proven to be one of the best methods to check the internal density concentrations of the stars predicted by theoretical models. During the main sequence phase, we have found a good agreement between the observed apsidal motion rates and computer-constructed stellar models provided that a realistic consideration is made of the evolution between the lower and upper borders of the main sequence (Giménez and García-Pelayo, 1982). An obvious extension of this work is a throughout study of the more evolved evolved systems beyond the TAMS where theoretical models are less accurate and empirical data from different sources are largely needed (see review paper by Zahn in this volume). A preliminary report on such a study is presented.

Statistical and Theoretical Models of Ingestion Through Turbine Rim Seals

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Kunyuan Zhou ◽  
Simon N. Wood ◽  
J. Michael Owen
Keyword(s):  
Experimental Data ◽  
Statistical Model ◽  
Flow Parameter ◽  
Likelihood Estimation ◽  
Theoretical Models ◽  
Operating Conditions ◽  
Data Points ◽  
Effects Of Rotation ◽  
Effectiveness Data ◽  
Good Agreement

In recent papers, orifice models have been developed to calculate the amount of ingestion, or ingress, that occurs through gas-turbine rim seals. These theoretical models can be used for externally induced (EI) ingress, where the pressure differences in the main gas path are dominant, and for rotationally induced (RI) ingress, where the effects of rotation in the wheel space are dominant. Explicit “effectiveness equations,” derived from the orifice models, are used to express the flow rate of sealing air in terms of the sealing effectiveness. These equations contain two unknown terms: Φmin, a sealing flow parameter, and Γc, the ratio of the discharge coefficients for ingress and egress. The two unknowns can be determined from concentration measurements in experimental rigs. In this paper, maximum likelihood estimation is used to fit the effectiveness equations to experimental data and to determine the optimum values of Φmin and Γc. The statistical model is validated numerically using noisy data generated from the effectiveness equations, and the simulated tests show the dangers of drawing conclusions from sparse data points. Using the statistical model, good agreement between the theoretical curves and several sets of previously published effectiveness data is achieved for both EI and RI ingress. The statistical and theoretical models have also been used to analyze previously unpublished experimental data, the results of which are included in separate papers. It is the ultimate aim of this research to apply the effectiveness data obtained at rig conditions to engine-operating conditions.

scholarly journals Effective Thermal Conductivity of Spherical Particulate Nanocomposites: Comparison with Theoretical Models, Monte Carlo Simulations and Experiments

2014 ◽  
Vol 13 (03) ◽  
pp. 1450022 ◽  
Author(s):  
Hatim Machrafi ◽  
Georgy Lebon
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Theoretical Models ◽  
Irreversible Thermodynamics ◽  
Flux Vector ◽  
Heat Flux Vector ◽  
The Matrix ◽  
The Status ◽  
Independent Variable ◽  
Good Agreement

The purpose of this work is to study heat conduction in systems that are composed out of spherical micro-and nanoparticles dispersed in a bulk matrix. Special emphasis will be put on the dependence of the effective heat conductivity on various selected parameters as dimension and density of particles, interface interaction with the matrix. This is achieved by combining the effective medium approximation and extended irreversible thermodynamics, whose main feature is to elevate the heat flux vector to the status of independent variable. The model is illustrated by three examples: Silicium-Germanium, Silica-epoxy-resin and Copper-Silicium systems. Predictions of our model are in good agreement with other theoretical models, Monte-Carlo simulations and experimental data.

Dual Role of Nanoparticles in the Thermal Conductivity Enhancement of Nanoparticle Suspensions

2005 ◽  
Author(s):  
Calvin H. Li ◽  
G. P. Peterson
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Brownian Motion ◽  
Theoretical Models ◽  
Conductivity Enhancement ◽  
Nanoparticle Suspensions ◽  
The Difference ◽  
Physical Phenomena ◽  
Good Agreement

Experimental evidence exists that the addition of a small quantity of nanoparticles to a base fluid, can have a significant impact on the effective thermal conductivity of the resulting suspension. The causes for this are currently thought to be due to a combination of two distinct mechanisms. The first is due to the change in the thermophysical properties of the suspension, resulting from the difference in the thermal conductivity of the fluid and the particles, and the second is thought to be due to the transport of thermal energy by the particles, due to the Brownian motion of the particles. In order to better understand these phenomena, a theoretical model has been developed that examines the effect of the Brownian motion. In this model, the well-known approach first presented by Maxwell, is combined with a new expression that incorporates the effect of the Brownian motion and describes the physical phenomena that occurs because of it. The results indicate that the enhanced thermal conductivity may not in fact be due to the transport of energy by the particles, but rather, due to the stirring motion caused by the movement of the nanoparticles which enhances the heat transfer within the fluid. The resulting model shows good agreement when compared with the existing experimental data and perhaps more importantly helps to explain the trends observed from a fundamental physical perspective. In addition, it provides a possible explanation for the differences that have been observed between the previously obtained experimental data, the predictions obtained from Maxwell’s equation and the theoretical models developed by other investigators.

scholarly journals Effect of Blade Cambering on Dynamic Stall in View of Designing Vertical Axis Turbines

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Pablo Ouro ◽  
Thorsten Stoesser ◽  
Luis Ramírez
Keyword(s):  
Vertical Axis ◽  
Dynamic Stall ◽  
Hysteresis Cycle ◽  
Aerodynamic Coefficients ◽  
Pitching Motion ◽  
Large Eddy ◽  
Naca 0012 ◽  
Drag Ratio ◽  
Lift To Drag Ratio ◽  
Good Agreement

This paper presents large eddy simulations (LESs) of symmetric and asymmetric (cambered) airfoils forced to undergo deep dynamic stall due to a prescribed pitching motion. Experimental data in terms of lift, drag, and moment coefficients are available for the symmetric NACA 0012 airfoil and these are used to validate the LESs. Good agreement between computed and experimentally observed coefficients is found confirming the accuracy of the method. The influence of foil asymmetry on the aerodynamic coefficients is analyzed by subjecting a NACA 4412 airfoil to the same flow and pitching motion conditions. Flow visualizations and analysis of aerodynamic forces allow an understanding and quantification of dynamic stall on both straight and cambered foils. The results confirm that cambered airfoils provide an increased lift-to-drag ratio and a decreased force hysteresis cycle in comparison to their symmetric counterparts. This may translate into increased performance and lower fatigue loads when using cambered airfoils in the design of vertical axis turbines (VATs) operating at low tip-speed ratios.

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