scholarly journals Numerical simulations of shock attenuation in solids and reevaluation of scaling law

2003 ◽  
Vol 108 (E1) ◽  
Author(s):  
Noriko K. Mitani
Keyword(s):  
Numerical Simulations ◽  
Scaling Law ◽  
Shock Attenuation

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 Mixing Driven by Radiative and Evaporative Cooling at the Stratocumulus Top

2015 ◽  
Vol 72 (12) ◽  
pp. 4681-4700 ◽  
Author(s):  
Alberto de Lozar ◽  
Juan Pedro Mellado
Keyword(s):  
Numerical Simulations ◽  
Scaling Laws ◽  
Scaling Law ◽  
Evaporative Cooling ◽  
Direct Numerical Simulations ◽  
Radiative Cooling ◽  
Grid Spacing ◽  
Inversion Point ◽  
Entrainment Velocity ◽  
Diffusive Effects

Abstract The stratocumulus-top mixing process is investigated using direct numerical simulations of a shear-free cloud-top mixing layer driven by evaporative and radiative cooling. An extension of previous linear formulations allows for quantifying radiative cooling, evaporative cooling, and the diffusive effects that artificially enhance mixing and evaporative cooling in high-viscosity direct numerical simulations (DNS) and many atmospheric simulations. The diffusive cooling accounts for 20% of the total evaporative cooling for the highest resolution (grid spacing ~14 cm), but this can be much larger (~100%) for lower resolutions that are commonly used in large-eddy simulations (grid spacing ~5 m). This result implies that the κ scaling for cloud cover might be strongly influenced by diffusive effects. Furthermore, the definition of the inversion point as the point of neutral buoyancy allows the derivation of two scaling laws. The in-cloud scaling law relates the velocity and buoyancy integral scales to a buoyancy flux defined by the inversion point. The entrainment-zone scaling law provides a relationship between the entrainment velocity and the liquid evaporation rate. By using this inversion point, it is shown that the radiative-cooling contribution to the entrainment velocity decouples from the evaporative-cooling contribution and behaves very similarly as in the smoke cloud. Finally, evaporative and radiative cooling have similar strengths, when this strength is measured by the integrated buoyancy source. This result partially explains why current entrainment parameterizations are not accurate enough, given that most of them implicitly assume that only one of the two mechanisms rules the entrainment.

A Scaling Law for Cavitation Inception in Circular Jet Flows

2007 ◽  
Author(s):  
Brian A. Edge ◽  
Eric G. Paterson ◽  
Mario F. Trujillo
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Scale Effects ◽  
Scaling Law ◽  
Pressure Coefficient ◽  
Cavitation Number ◽  
Scaling Relations ◽  
Length Scale ◽  
Cavitation Inception ◽  
Dynamic Head

The historical data for circular jets indicates that the incipient cavitation number increases with the diameter of the jet. This trend is not explained by the classic cavitation theory which expects incipient cavitation number to remain constant regardless of the jet diameter, flow parameters, or water quality. This paper explores the origins of cavitation scale effects and explains the correlation between the incipient cavitation number, jet diameter, and nuclei size. This is accomplished through turbulence-resolving CFD simulations of the jet flow field at three length scales and Rayleigh-Plesset bubble dynamics for three nuclei sizes. The numerical simulations show that incipient cavitation number (σi) changes significantly as the size of the jet is altered while the Reynolds number and the value of the minimum pressure coefficient are held constant. Larger nuclei bubbles (100μm) exhibit an increase in σi with jet diameter, while moderate (50μm) and small (10μm) nuclei bubble exhibit a decrease in σi as jet diameter increases. The value of σi associated with a small jet was similar for all nuclei sizes. As the jet increased in size, the disparity between the values of σi associated with each nuclei size was found to increase substantially. The equilibrium form of the Rayleigh-Plesset equation was used to derive a correction to the classic theory of cavitation inception. This correction is a function of initial nuclei size and the dynamic head of the flow. As either the nuclei properties or dynamic head of the fluid change, the magnitude of the correction term will also change. This correction to the classic cavitation theory was used to make predictions of how σi will change as length scale and Reynolds number are altered. These equilibrium predictions were found to be in good agreement with the numerical simulations of cavitation inception for large and moderate (100μm and 50μm) nuclei bubbles. Comparisons with the small (10μm) nuclei bubbles indicate that the inertial terms are quite significant for these bubbles, resulting in large discrepancies between the full numerical solution and the equilibrium predictions. In general, the equilibrium scaling relations show that as the length scale of a flow is held constant and the Reynolds number is increased, σi will converge to −CPmin. The scaling relations also show that when Reynolds number is held constant and the length scale of a flow is increased, σi will depart from −CPmin.

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 Layering and turbulence surrounding an anticyclonic oceanic vortex: in situ observations and quasi-geostrophic numerical simulations

2013 ◽  
Vol 731 ◽  
pp. 418-442 ◽  
Author(s):  
Bach Lien Hua ◽  
Claire Ménesguen ◽  
Sylvie Le Gentil ◽  
Richard Schopp ◽  
Bruno Marsset ◽  
...  
Keyword(s):  
Potential Energy ◽  
Numerical Simulations ◽  
Potential Vorticity ◽  
Scaling Law ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Critical Levels ◽  
Vertical Derivative ◽  
Vertical Scales

AbstractEvidence of persistent layering, with a vertical stacking of sharp variations in temperature, has been presented recently at the vertical and lateral periphery of energetic oceanic vortices through seismic imaging of the water column. The stacking has vertical scales ranging from a few metres up to 100 m and a lateral spatial coherence of several tens of kilometres comparable with the vortex horizontal size. Inside this layering, in situ data display a $[{ k}_{h}^{- 5/ 3} { k}_{h}^{- 2} ] $ scaling law of horizontal scales for two different quantities, temperature and a proxy for its vertical derivative, but for two different ranges of wavelengths, between 5 and 50 km for temperature and between 500 m and 5 km for its vertical gradient. In this study, we explore the dynamics underlying the layering formation mechanism, through the slow dynamics captured by quasi-geostrophic equations. Three-dimensional high-resolution numerical simulations of the destabilization of a lens-shaped vortex confirm that the vertical stacking of sharp jumps in density at its periphery is the three-dimensional analogue of the preferential wind-up of potential vorticity near a critical radius, a phenomenon which has been documented for barotropic vortices. For a small-Burger (flat) lens vortex, baroclinic instability ensures a sustained growth rate of sharp jumps in temperature near the critical levels of the leading unstable modes. Such results can be obtained for a background stratification which is due to temperature only and does not require the existence of salt anomalies. Aloft and beneath the vortex core, numerical simulations well reproduce the $[{ k}_{h}^{- 5/ 3} { k}_{h}^{- 2} ] $ scaling law of horizontal scales for the vertical derivative of temperature that is observed in situ inside the layering, whatever the background stratification. Such a result stems from the tracer-like behaviour of the vortex stretching component and previous studies have shown that spectra of tracer fields can be steeper than $- 1$, namely in $- 5/ 3$ or $- 2$, if the advection field is very compact spatially, with a $- 5/ 3$ slope corresponding to a spiral advection of the tracer. Such a scaling law could thus be of geometric origin. As for the kinetic and potential energy, the ${ k}_{h}^{- 5/ 3} $ scaling law can be reproduced numerically and is enhanced when the background stratification profile is strongly variable, involving sharp jumps in potential vorticity such as those observed in situ. This raises the possibility of another plausible mechanism leading to a $- 5/ 3$ scaling law, namely surface-quasi-geostrophic (SQG)-like dynamics, although our set-up is more complex than the idealized SQG framework. Energy and enstrophy fluxes have been diagnosed in the numerical quasi-geostrophic simulations. The results emphasize a strong production of energy in the oceanic submesoscales range and a kinetic and potential energy flux from mesoscale to submesoscales range near the critical levels. Such horizontal submesoscale production, which is correlated to the accumulation of thin vertical scales inside the layering, thus has a significant slow dynamical component, well-captured by quasi-geostrophy.

Erosion and accretion by cratering impacts on rocky and icy bodies: Formulation of scaling relations for high-speed ejecta

2021 ◽  
Author(s):  
Hidenori Genda ◽  
Ryuki Hyodo
Keyword(s):  
Point Source ◽  
Numerical Simulations ◽  
High Speed ◽  
Scaling Law ◽  
Large Body ◽  
Target Material ◽  
Target Surface ◽  
Impact Angle ◽  
Material Strength ◽  
The Impact

<p>Numerous small bodies inevitably lead to cratering impacts on large planetary bodies during planet formation and evolution. As a consequence of these small impacts, a fraction of the target material escapes from the gravity of the large body, and a fraction of the impactor material accretes onto the target surface, depending on the impact velocities and angles. Here, we study the mass of the high-speed ejecta that escapes from the target gravity by cratering impacts when material strength is neglected. We perform a large number of cratering impact simulations onto a planar rocky and icy targets using the smoothed particle hydrodynamics method. We show that the escape mass of the target material obtained from our numerical simulations agrees with the prediction of a scaling law under a point-source assumption when <em>v</em><sub>imp</sub> > ~ 10 <em>v</em><sub>esc</sub>, where <em>v</em><sub>imp</sub> is the impact velocity and <em>v</em><sub>esc</sub> is the escape velocity of the target. However, we find that the point-source scaling law overestimates the escape mass up to a factor of ~ 70, depending on the impact angle, when <em>v</em><sub>imp</sub> < ~ 10 <em>v</em><sub>esc</sub> (Figure 1). Using data obtained from numerical simulations, we derive a new scaling law for the escape mass of the target material

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

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