scholarly journals Triadic resonances in precessing rapidly rotating cylinder flows

2015 ◽  
Vol 778 ◽  
Author(s):  
T. Albrecht ◽  
H. M. Blackburn ◽  
J. M. Lopez ◽  
R. Manasseh ◽  
P. Meunier
Keyword(s):  
Rotating Cylinder ◽  
Direct Numerical Simulations ◽  
Mode Shapes ◽  
Resonance Model ◽  
Rapid Rotation ◽  
Nutation Angle ◽  
Resonant Instability ◽  
Theoretical Predictions ◽  
Long Time ◽  
Good Agreement

Direct numerical simulations of flows in cylinders subjected to both rapid rotation and axial precession are presented and analysed in the context of a stability theory based on the triadic resonance of Kelvin modes. For a case that was chosen to provide a finely tuned resonant instability with a small nutation angle, the simulations are in good agreement with the theory and previous experiments in terms of mode shapes and dynamics, including long-time-scale regularization of the flow and recurrent collapses. Cases not tuned to the most unstable triad, but with the nutation angle still small, are also in quite good agreement with theoretical predictions, showing that the presence of viscosity makes the physics of the triadic-resonance model robust to detuning. Finally, for a case with $45^{\circ }$ nutation angle for which it has been suggested that resonance does not occur, the simulations show that a slowly growing triadic resonance predicted by theory is in fact observed if sufficient evolution time is allowed.

scholarly journals Asymmetry of vertical buoyancy gradient in stratified turbulence

2019 ◽  
Vol 870 ◽  
pp. 266-289
Author(s):  
Andrea Maffioli
Keyword(s):  
Numerical Simulations ◽  
Isotropic Turbulence ◽  
Vertical Direction ◽  
Direct Consequence ◽  
Stable Stratification ◽  
Direct Numerical Simulations ◽  
Stratified Turbulence ◽  
Theoretical Predictions ◽  
Rapid Adjustment ◽  
Good Agreement

We consider the asymmetry of the buoyancy field in the vertical direction in stratified turbulence. While this asymmetry is known, its causes are not well understood, and it has not been systematically quantified previously. Using theoretical arguments, it is shown that both stratified turbulence and isotropic turbulence in the presence of a mean scalar gradient will become positively skewed, as a direct consequence of the presence of stratification and mean scalar gradient, respectively. Assuming a rapid adjustment of isotropic turbulence to a stable stratification on a time scale $\unicode[STIX]{x1D70F}\sim N^{-1}$, where $N$ is the Brunt–Väisälä frequency, a scaling for the skewness of the vertical buoyancy gradient is obtained. Direct numerical simulations of stratified turbulence with forcing are performed and the positive skewness of $\unicode[STIX]{x2202}b/\unicode[STIX]{x2202}z$ is confirmed ($b$ is the buoyancy). Both the volume-averaged dimensional skewness, $\langle (\unicode[STIX]{x2202}b/\unicode[STIX]{x2202}z)^{3}\rangle$, and the non-dimensional skewness, $S$, are computed and compared against the theoretical predictions. There is a good agreement for $\langle (\unicode[STIX]{x2202}b/\unicode[STIX]{x2202}z)^{3}\rangle$, while there is a discrepancy in the behaviour of $S$. The theory predicts $S\sim 1$ and a constant skewness, while the direct numerical simulations confirm that the skewness is $O(1)$ but with a remaining dependence on the Froude number. The results are interpreted as being due to the concurrent action of linear and nonlinear processes in stratified turbulence leading to $S>0$ and to the formation of layers and interfaces in vertical profiles of buoyancy.

scholarly journals Type II migration strikes back – an old paradigm for planet migration in discs

2019 ◽  
Vol 492 (1) ◽  
pp. 1318-1328 ◽  
Author(s):  
Chiara E Scardoni ◽  
Giovanni P Rosotti ◽  
Giuseppe Lodato ◽  
Cathie J Clarke
Keyword(s):  
Initial Conditions ◽  
Giant Planet ◽  
Type Ii ◽  
Standard Type ◽  
Planet Migration ◽  
Theoretical Predictions ◽  
Gap Opening ◽  
Long Time ◽  
Flow Through ◽  
Good Agreement

ABSTRACT In this paper, we analyse giant gap-opening planet migration in proto-planetary discs, focusing on the type II migration regime. According to standard type II theory, planets migrate at the same rate as the gas in the disc, as they are coupled to the disc viscous evolution; however, recent studies questioned this paradigm, suggesting that planets migrate faster than the disc material. We study the problem through 2D long-time simulations of systems consistent with type II regime, using the hydrodynamical grid code fargo3d. Even though our simulations confirm the presence of an initial phase characterized by fast migration, they also reveal that the migration velocity slows down and eventually reaches the theoretical prediction if we allow the system to evolve for enough time. We find the same tendency to evolve towards the theoretical predictions at later times when we analyse the mass flow through the gap and the torques acting on the planet. This transient is related to the initial conditions of our (and previous) simulations, and is due to the fact that the shape of the gap has to adjust to a new profile, once the planet is set into motion. Secondly, we test whether the type II theory expectation that giant planet migration is driven by viscosity is consistent with our simulation by comparing simulations with the same viscosity and different disc masses (or vice versa). We find a good agreement with the theory, since when the discs are characterized by the same viscosity, the migration properties are the same.

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

Dynamic model for high-speed rotors based on their experimental characterization

2017 ◽  
Vol 2 (4) ◽  
pp. 25
Author(s):  
L. A. Montoya ◽  
E. E. Rodríguez ◽  
H. J. Zúñiga ◽  
I. Mejía
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Experimental Characterization ◽  
Rotating Systems ◽  
Computing Performance ◽  
The Impact ◽  
Stiffness Distribution ◽  
Good Agreement

Rotating systems components such as rotors, have dynamic characteristics that are of great importance to understand because they may cause failure of turbomachinery. Therefore, it is required to study a dynamic model to predict some vibration characteristics, in this case, the natural frequencies and mode shapes (both of free vibration) of a centrifugal compressor shaft. The peculiarity of the dynamic model proposed is that using frequency and displacements values obtained experimentally, it is possible to calculate the mass and stiffness distribution of the shaft, and then use these values to estimate the theoretical modal parameters. The natural frequencies and mode shapes of the shaft were obtained with experimental modal analysis by using the impact test. The results predicted by the model are in good agreement with the experimental test. The model is also flexible with other geometries and has a great time and computing performance, which can be evaluated with respect to other commercial software in the future.

scholarly journals A Generalized Approach for Evaluating the Mechanical Properties of Polymer Nanocomposites Reinforced with Spherical Fillers

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 830
Author(s):  
Julio Cesar Martinez-Garcia ◽  
Alexandre Serraïma-Ferrer ◽  
Aitor Lopeandía-Fernández ◽  
Marco Lattuada ◽  
Janak Sapkota ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Polymeric Nanocomposites ◽  
Mechanical Reinforcement ◽  
Future Studies ◽  
Three Phase ◽  
Theoretical Predictions ◽  
Filler Network ◽  
New Research ◽  
Good Agreement ◽  
Research Avenue

In this work, the effective mechanical reinforcement of polymeric nanocomposites containing spherical particle fillers is predicted based on a generalized analytical three-phase-series-parallel model, considering the concepts of percolation and the interfacial glassy region. While the concept of percolation is solely taken as a contribution of the filler-network, we herein show that the glassy interphase between filler and matrix, which is often in the nanometers range, is also to be considered while interpreting enhanced mechanical properties of particulate filled polymeric nanocomposites. To demonstrate the relevance of the proposed generalized equation, we have fitted several experimental results which show a good agreement with theoretical predictions. Thus, the approach presented here can be valuable to elucidate new possible conceptual routes for the creation of new materials with fundamental technological applications and can open a new research avenue for future studies.

The Reduction of Bias Error in Transfer Function Estimates Using FFT-Based Analyzers

1984 ◽  
Vol 106 (1) ◽  
pp. 29-35 ◽  
Author(s):  
P. Cawley
Keyword(s):  
Transfer Function ◽  
Random Excitation ◽  
Analogue Computer ◽  
Bias Error ◽  
Testing Time ◽  
Theoretical Predictions ◽  
Set Up ◽  
Modal Mass ◽  
Time Required ◽  
Good Agreement

The susceptibility to bias error of two methods for computing transfer (frequency response) functions from spectra produced by FFT-based analyzers using random excitation has been investigated. Results from tests with an FFT analyzer on a single degree-of-freedom system set up on an analogue computer show good agreement with the theoretical predictions. It has been shown that, around resonance, the bias error in the transfer function estimate H2 (Syy/Sxy*) is considerably less than that in the more commonly used estimate, H1 (Sxy/Sxx). The record length, and hence the testing time, required for a given accuracy is reduced by over 50 percent if the H2 calculation procedure is used. The analysis has also shown that if shaker excitation is used on lightly damped structures with low modal mass, it is important to minimize the mass of the force gage and the moving element of the shaker.

Investigating the vibrational behaviour of a rotating two-blade propeller by using a self-tracking method

2018 ◽  
Vol 233 (3) ◽  
pp. 835-847 ◽  
Author(s):  
Mohammad-Reza Ashory ◽  
Farhad Talebi ◽  
Heydar R Ghadikolaei ◽  
Morad Karimpour
Keyword(s):  
Natural Frequency ◽  
Measurement Errors ◽  
Mode Shapes ◽  
Model Parameters ◽  
Test Results ◽  
Modal Assurance Criterion ◽  
Tracking Method ◽  
Strong Resemblance ◽  
Test Scenarios ◽  
Good Agreement

This study investigated the vibrational behaviour of a rotating two-blade propeller at different rotational speeds by using self-tracking laser Doppler vibrometry. Given that a self-tracking method necessitates the accurate adjustment of test setups to reduce measurement errors, a test table with sufficient rigidity was designed and built to enable the adjustment and repair of test components. The results of the self-tracking test on the rotating propeller indicated an increase in natural frequency and a decrease in the amplitude of normalized mode shapes as rotational speed increases. To assess the test results, a numerical model created in ABAQUS was used. The model parameters were tuned in such a way that the natural frequency and associated mode shapes were in good agreement with those derived using a hammer test on a stationary propeller. The mode shapes obtained from the hammer test and the numerical (ABAQUS) modelling were compared using the modal assurance criterion. The examination indicated a strong resemblance between the hammer test results and the numerical findings. Hence, the model can be employed to determine the other mechanical properties of two-blade propellers in test scenarios.

Fluid Added Mass Effect in the Modal Response of a Pump-Turbine Impeller

2009 ◽  
Author(s):  
Eduard Egusquiza ◽  
Carme Valero ◽  
Quanwei Liang ◽  
Miguel Coussirat ◽  
Ulrich Seidel
Keyword(s):  
Natural Frequencies ◽  
Experimental Tests ◽  
Mass Effect ◽  
Added Mass ◽  
Mode Shapes ◽  
Pump Turbine ◽  
Modal Response ◽  
Surrounding Fluid ◽  
Turbine Impeller ◽  
Good Agreement

In this paper, the reduction in the natural frequencies of a pump-turbine impeller prototype when submerged in water has been investigated. The impeller, with a diameter of 2.870m belongs to a pump-turbine unit with a power of around 100MW. To analyze the influence of the added mass, both experimental tests and numerical simulations have been carried out. The experiment has been performed in air and in water. From the frequency response functions the modal characteristics such as natural frequencies and mode shapes have been obtained. A numerical simulation using FEM (Finite Elements Model) was done using the same boundary conditions as in the experiment (impeller in air and surrounded by a mass of water). The modal behaviour has also been calculated. The numerical results were compared with the available experimental results. The comparison shows a good agreement in the natural frequency values both in air and in water. The reduction in frequency due to the added mass effect of surrounding fluid has been calculated. The physics of this phenomenon due to the fluid structure interaction has been investigated from the analysis of the mode-shapes.

Theoretical Prediction of Motions of High-Speed Planing Boats in Waves

1978 ◽  
Vol 22 (03) ◽  
pp. 140-169
Author(s):  
Milton Martin
Keyword(s):  
High Speed ◽  
Damping Ratio ◽  
Nonlinear Effects ◽  
Theoretical Method ◽  
Valuable Insight ◽  
Response Characteristics ◽  
Theoretical Predictions ◽  
Response Amplitude Operators ◽  
Phase Angles ◽  
Good Agreement

A theoretical method is derived for predicting the linearized response characteristics of constant deadrise high-speed planing boats in head and following waves. Comparisons of the theoretical predictions of the pitch and heave response amplitude operators and phase angles with existing experimental data show reasonably good agreement for a wide variety of conditions of interest. It appears that nonlinear effects are more severe at a speed to length ratio of 6 than of, say, 4 or less, principally because of the reduction of the damping ratio of the boat with increasing speed, and the consequent increase in motions in the vicinity of the resonant encounter frequency. However, it is concluded that the linear theory can provide a simple and fast means of determining the effect of various parameters such as trim angle, deadrise, loading, and speed on the damping, natural frequency, and linearized response in waves, and that this can furnish valuable insight into the actual boat dynamics, even though the accurate predictions of large motions and peak accelerations would require a nonlinear analysis.

On Wall Effects in Cavity Flows

1984 ◽  
Vol 28 (01) ◽  
pp. 70-75
Author(s):  
C. C. Hsu
Keyword(s):  
Numerical Results ◽  
Cavity Flows ◽  
Two Dimensional ◽  
Wall Effects ◽  
Free Jet ◽  
Theoretical Predictions ◽  
Experimental Findings ◽  
Good Agreement

Simple wall correction rules for two-dimensional and nearly two-dimensional cavity flows in closed or free jet water tunnels, based on existing linearized analyses, are made. Numerical results calculated from these expressions are compared with existing experimental findings. The present theoretical predictions are, in general, in good agreement with data.

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