Shock-wave surfing

2011 ◽  
Vol 676 ◽  
pp. 396-431 ◽  
Author(s):  
S. J. LAURENCE ◽  
R. DEITERDING
Keyword(s):  
Shock Wave ◽  
Numerical Simulations ◽  
Analytical Model ◽  
Large Fraction ◽  
Scaling Law ◽  
Parent Body ◽  
Radius Ratio ◽  
Lateral Velocity ◽  
Complex Situation ◽  
Separation Velocity

A phenomenon referred to as ‘shock-wave surfing’, in which a body moves in such a way as to follow the shock wave generated by another upstream body, is investigated numerically and analytically. During the surfing process, the downstream body can accumulate a significantly higher lateral velocity than would otherwise be possible. The surfing effect is first investigated for interactions between a sphere and a planar oblique shock. Numerical simulations are performed and a simple analytical model is developed to determine the forces acting on the sphere. A phase-plane description is employed to elucidate features of the system dynamics. The analytical model is then generalised to the more complex situation of aerodynamic interactions between two spheres, and, through comparisons with further computations, is shown to adequately predict the final separation velocity of the surfing sphere in initially touching configurations. Both numerical simulations and a theoretical analysis indicate a strong influence of the sphere radius ratio on the separation process and predict a critical radius ratio that delineates entrainment of the smaller body within the flow region bounded by the larger body's shock from expulsion. Furthermore, it is shown that an earlier scaling law does not accurately describe the separation behaviour. The surfing effect has important implications for meteoroid fragmentation: in particular, a large fraction of the variation in the separation velocity deduced by previous authors from an analysis of terrestrial crater fields can be explained by a combination of surfing and a modest rotation rate of the parent body.

scholarly journals The Impact of Initial Conditions in N-Body Simulations of Debris Discs

2015 ◽  
Vol 32 ◽  
Author(s):  
E. Thilliez ◽  
S. T. Maddison
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Parent Body ◽  
Dust Trapping ◽  
Physical Context ◽  
Disc Width ◽  
Wide Range ◽  
Belt Width ◽  
New Generation ◽  
The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

The effects of geometric offsets on the dynamic responses of a Scott—Russell amplifying mechanism with flexible hinges

2009 ◽  
Vol 223 (10) ◽  
pp. 2413-2423 ◽  
Author(s):  
C-M Chen ◽  
R-F Fung
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
Dynamic Responses ◽  
Analytical Models ◽  
Dynamic Equations ◽  
Magnification Factor ◽  
Flexure Hinges ◽  
Magnification Factors ◽  
Straight Line ◽  
Deviation Factor

The dynamic equations of a micro-positioning Scott—Russell (SR) mechanism associated with two flexible hinges and an offset are developed to calculate output responses. Both rigid and flexible hinges are considered to explore the results. The main features in the kinematics of the SR mechanism are its displacement amplification and straight-line motion, which are widely needed in practical industries. The manufacturing inaccuracy of the SR mechanism definitely causes geometric offsets of flexure hinges, and affects displacement amplification and straight-line output motion. Analytical models based on kinematics and Hamilton's principle are derived to explore the variation of linearity ratio, magnification factor, and deviation factor due to various offsets and link lengths. From numerical simulations for the SR mechanism with various offsets of flexible hinges in the conditions of different link lengths, it is found that offsets of flexure hinges obviously affect the amplifying factor and linearity ratio, and appear to dominate the changes of magnification factors. Moreover, an analytical model is also used to predict magnification factors due to various offsets. Finally, some conclusions concerning the effects of offset on the performance of the SR mechanism are drawn.

Tank Test and Numerical Simulation of Spar Type Floating OTEC

2021 ◽  
Author(s):  
Shunka C. Hirao ◽  
Jun Umeda ◽  
Kentaroh Kokubun ◽  
Toshifumi Fujiwara
Keyword(s):  
Numerical Simulations ◽  
Cold Water ◽  
Scaling Law ◽  
Internal Flow ◽  
Bending Moment ◽  
Floating Structure ◽  
Waves And Currents ◽  
Tank Test ◽  
Safety Assessments ◽  
Ocean Thermal Energy

Abstract National Maritime Research Institute, NMRI, had been studying the analytical method on safety assessments of floating power generation facilities for ten years more. As a part of these studies, an Ocean Thermal Energy Conversion (OTEC) was also studied in our institute. The OTEC normally has a very long and thick Cold-Water Pipe (CWP) with an unanchored end to pump up a large amount of cold-water continuously. From the viewpoints of the safety assessments of the OTEC operation, it is noteworthy to confirm the effect of the existing long pipe against a floating unit/body and an effect of internal flowing water. It is necessary, moreover, to consider the Vortex Induced Vibration (VIV) effect for floater motions and structural analysis of the pipe itself and a connecting point of the floating structure. In this paper, the results of model tests and numerical simulations of a spar type floating OTEC with a single CWP in waves and currents are presented. The CWP model was made of material fitting the scaling law for a planned full scale OTEC. The specific and unique phenomena of the floating OTEC were confirmed from the model test results. Based on the results of the tank tests and the numerical simulations, we confirmed the necessary items and arrangements for safety evaluations. In detail, the internal flow increased the bending moment at the connection point.

scholarly journals On the Scaling of Bubble Cluster Collapse in Cloud Cavitating Flow Around a Slender Projectile

2015 ◽  
Author(s):  
Yiwei Wang ◽  
Chenguang Huang ◽  
Xiaocui Wu
Keyword(s):  
Phase Change ◽  
Numerical Simulations ◽  
Scaling Law ◽  
Cavitating Flow ◽  
Cavitation Model ◽  
Bubble Cluster ◽  
Collapse Pressure ◽  
Variation Range ◽  
Main Factors ◽  
Similarity Law

The scaling law of bubble cluster collapse in cloud cavitating flow around a slender projectile is investigated in the present paper. The influence of compressibility is mainly discussed. Firstly the governing parameters are obtained by dimensional analysis, and the numerical method is established in order to verify the similarity law and obtain the influence of parameters based on a mixture approach with Singhal cavitation model. Moreover, the similarity law is validated by numerical simulations. Two main factors of compressibility of mixture fluid, including compressibility of non-condensable gas and phase change, are studied, respectively. Results indicated that the phase change has little influence on both flowing and collapse pressure. In the condition that the variation range of the mixture compressibility is small, the compressibility of non-condensable gas has notable impact the local collapse pressure peaks, however the macroscopic flow pattern does not change.

scholarly journals Approximate Analytical Models of Shock-Wave Structure at Steady Mach Reflection

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 305
Author(s):  
Mikhail V. Chernyshov ◽  
Karina E. Savelova ◽  
Anna S. Kapralova
Keyword(s):  
Experimental Data ◽  
Shock Wave ◽  
Comparative Analysis ◽  
Analytical Model ◽  
Mach Reflection ◽  
Supersonic Jet ◽  
Wave Structure ◽  
Analytical Models ◽  
Analytical Prediction ◽  
Shock Wave Structure

In this study, we obtain the comparative analysis of methods of quick approximate analytical prediction of Mach shock height in planar steady supersonic flows (for example, in supersonic jet flow and in narrowing channel between two wedges), that are developed since the 1980s and being actively modernized now. A new analytical model based on flow averaging downstream curved Mach shock is proposed, which seems more accurate than preceding models, comparing with numerical and experimental data.

scholarly journals Analysis of an Approximated Model for the Depletion Region Width of Planar Junctionless Transistors

Electronics ◽  
2019 ◽  
Vol 8 (12) ◽  
pp. 1436
Author(s):  
Arian Nowbahari ◽  
Avisek Roy ◽  
Muhammad Nadeem Akram ◽  
Luca Marchetti
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
Threshold Voltage ◽  
Analytical Formula ◽  
Numerical Data ◽  
Maximum Error ◽  
Depletion Region ◽  
Comsol Multiphysics ◽  
Flat Band ◽  
Junctionless Transistors

In this paper, we investigate the accuracy of the approximated analytical model currently utilized, by many researchers, to describe the depletion region width in planar junctionless transistors (PJLT). The proposed analysis was supported by numerical simulations performed in COMSOL Multiphysics software. By comparing the numerical results and the approximated analytical model of the depletion region width, we calculated that the model introduces a maximum RMS error equal to 90 % of the donor concentration in the substrate. The maximum error is achieved when the gate voltage approaches the threshold voltage ( V t h ) or when it approaches the flat band voltage ( V F B ) of the transistor. From these results, we concluded that this model cannot be used to determine accurately the flat-band and the threshold voltage of the transistor, although it represents a straightforward method to estimate the depletion region width in PJLT. By using the approximated analytical model, we extracted an analytical formula, which describes the electron concentration at the ideal boundary of the depletion region. This formula approximates the numerical data extracted from COMSOL with a relative error lower than 1 % . The proposed formula is in our opinion, as useful as the formula of the approximated analytical model because it allows for estimating the position of the depletion region also when the drain and source terminals are not grounded. We concluded that the analytical formula proposed at the end of this work could be useful to determine the position of the depletion region boundary in numerical simulations and in graphical representations provided by COMSOL Multiphysics software.

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