scholarly journals Dispersive shock waves in viscously deformable media

2013 ◽  
Vol 718 ◽  
pp. 524-557 ◽  
Author(s):  
Nicholas K. Lowman ◽  
M. A. Hoefer
Keyword(s):  
Shock Waves ◽  
Volume Fraction ◽  
Initial Conditions ◽  
Leading Edge ◽  
Wave Dispersion ◽  
Cross Sectional ◽  
Theoretical Predictions ◽  
Number Dynamics ◽  
Long Time ◽  
Constitutive Parameters

AbstractThe viscously dominated, low-Reynolds-number dynamics of multi-phase, compacting media can lead to nonlinear, dissipationless/dispersive behaviour when viewed appropriately. In these systems, nonlinear self-steepening competes with wave dispersion, giving rise to dispersive shock waves (DSWs). Example systems considered here include magma migration through the mantle as well as the buoyant ascent of a low-density fluid through a viscously deformable conduit. These flows are modelled by a third-order, degenerate, dispersive, nonlinear wave equation for the porosity (magma volume fraction) or cross-sectional area, respectively. Whitham averaging theory for step initial conditions is used to compute analytical, closed-form predictions for the DSW speeds and the leading edge amplitude in terms of the constitutive parameters and initial jump height. Novel physical behaviours are identified including backflow and DSW implosion for initial jumps sufficient to cause gradient catastrophe in the Whitham modulation equations. Theoretical predictions are shown to be in excellent agreement with long-time numerical simulations for the case of small- to moderate-amplitude DSWs. Verifiable criteria identifying the breakdown of this modulation theory in the large jump regime, applicable to a wide class of DSW problems, are presented.

scholarly journals Waves reflected by solid wall in the mixture of liquid with vapour bubbles

2002 ◽  
Vol 24 (3) ◽  
pp. 167-180
Author(s):  
Duong Ngoc Hai ◽  
Nguyen Van Tuan
Keyword(s):  
Shock Waves ◽  
Volume Fraction ◽  
Initial Conditions ◽  
Solid Wall ◽  
Vapour Phase ◽  
Gas Mixtures ◽  
Industrial Processes ◽  
Shock Strength ◽  
Stationary Shock ◽  
The Waves

The liquid and gas mixtures are met in many natural and industrial processes. In the paper the results of investigation of waves reflected by solid wall of the stationary shock waves with moderate intensities or the transient pulses propagated in the mixture of liquid with vapour bubbles are presented. The effect of initial conditions, shock strength, size of the bubbles and volume fraction of vapour phase on the behaviour of the waves reflected by solid wall is studied.

Shock Waves in Liquids With Bubbles Containing Evaporating Drops

2000 ◽  
Author(s):  
Nail S. Khabeev ◽  
Arnold F. Bertelsen ◽  
Oleg R. Ganiev
Keyword(s):  
Shock Waves ◽  
Static Pressure ◽  
Volume Fraction ◽  
Initial Conditions ◽  
Wave Structure ◽  
Physical Parameters ◽  
Volume Changes ◽  
Wave Processes ◽  
Steady Shock ◽  
Evaporating Drops

Abstract An investigation of wave processes in liquids with bubbles containing evaporating drops is presented. A model is used which takes into account both the liquid radial inertia due to medium volume changes, and the temperature distribution inside and around the bubbles. An analysis of the microsopic fields of physical parameters is aimed at closing the system of equations for averaged characteristics. The evolution of non-steady shock waves in liquids with bubbles containing evaporating drops is studied by numerical methods. The effect of the initial conditions, shock strength, volume fraction, dispersity of the vapor phase, initial static pressure and of the thermophysical properties of the phases on shock-wave structure and evolution is studied. The possible enhancement of disturbances in the region of their initiation is shown. The phenomenon of the nonlinear anomalous enhancement of waves reflected from a wall is established.

Understanding evolution of vortex rings in viscous fluids

2017 ◽  
Vol 836 ◽  
pp. 873-909 ◽  
Author(s):  
Aashay Tinaikar ◽  
S. Advaith ◽  
S. Basu
Keyword(s):  
High Speed ◽  
Initial Conditions ◽  
Operating Conditions ◽  
Force Balance ◽  
Vortex Rings ◽  
Time Behaviour ◽  
Theoretical Predictions ◽  
Long Time ◽  
Vortex Size ◽  
Short Time

The evolution of vortex rings in isodensity and isoviscosity fluid has been studied analytically using a novel mathematical model. The model predicts the spatiotemporal variation in peak vorticity, circulation, vortex size and spacing based on instantaneous vortex parameters. This proposed model is quantitatively verified using experimental measurements. Experiments are conducted using high-speed particle image velocimetry (PIV) and laser induced fluorescence (LIF) techniques. Non-buoyant vortex rings are generated from a nozzle using a constant hydrostatic pressure tank. The vortex Reynolds number based on circulation $(\unicode[STIX]{x1D6E4}/\unicode[STIX]{x1D708})$ is varied in the range 100–1500 to account for a large range of operating conditions. Experimental results show good agreement with theoretical predictions. However, it is observed that neither Saffman’s thin-core model nor the thick-core equations could correctly explain vortex evolution for all initial conditions. Therefore, a transitional theory is framed using force balance equations which seamlessly integrate short- and long-time asymptotic theories. It is found that the parameter $A=(a/\unicode[STIX]{x1D70E})^{2}$, where $a$ is the vortex half-spacing and $\unicode[STIX]{x1D70E}$ denotes the standard deviation of the Gaussian vorticity profile, governs the regime of vortex evolution. For higher values of $A$, evolution follows short-time behaviour, while for $A=O(1)$, long-time behaviour is prominent. Using this theory, many reported anomalous observations have been explained.

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.

Flow Structure Near the Bow of a Two-Dimensional Body

1989 ◽  
Vol 33 (04) ◽  
pp. 269-283
Author(s):  
Mark A. Grosenbaugh ◽  
Ronald W. Yeung
Keyword(s):  
Free Surface ◽  
Power Spectra ◽  
Leading Edge ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Bow Wave ◽  
Wave Elevation ◽  
Characteristic Oscillation ◽  
Theoretical Predictions ◽  
Sectional Shape

Flow near a blunt ship's bow is experimentally investigated by studying the flow in front of horizontal, surface-piercing cylinders. A bore-like structure develops at the bow of a cylinder when it is immersed in a uniform stream. Observations indicate that the leading edge of this bow wave coincides with a point at which the main flow separates from the free surface. Experimental measurements of the location of the wavefront and the slope of the free surface at the wavefront are in fair agreement with existing theoretical predictions. Power spectra of the time records of the bow-wave elevation show a characteristic oscillation frequency at Froude numbers above a critical value. The bow-wave oscillation is a function of the cross-sectional shape of the two-dimensional body, the draft, and, to a lesser extent, the flow velocity. The inception of the oscillation depends on the Reynolds number, but the characteristic frequency is governed by inertial and gravitational forces.

The stabilization of B.C.C. Cu in Cu/Nb nanolayered composites

1996 ◽  
Vol 54 ◽  
pp. 228-229
Author(s):  
H. Kung ◽  
A.J. Griffin ◽  
Y.C. Lu ◽  
K.E. Sickafus ◽  
T.E. Mitchell ◽  
...  
Keyword(s):  
Electrical Resistivity ◽  
Layer Thickness ◽  
Volume Fraction ◽  
Ion Beam ◽  
High Strength ◽  
Cross Sectional ◽  
Metastable Structure ◽  
High Resolution Tem ◽  
Potential Improvement ◽  
Two Phases

Materials with compositionally modulated structures have gained much attention recently due to potential improvement in electrical, magnetic and mechanical properties. Specifically, Cu-Nb laminate systems have been extensively studied mainly due to the combination of high strength, and superior thermal and electrical conductivity that can be obtained and optimized for the different applications. The effect of layer thickness on the hardness, residual stress and electrical resistivity has been investigated. In general, increases in hardness and electrical resistivity have been observed with decreasing layer thickness. In addition, reduction in structural scale has caused the formation of a metastable structure which exhibits uniquely different properties. In this study, we report the formation of b.c.c. Cu in highly textured Cu/Nb nanolayers. A series of Cu/Nb nanolayered films, with alternating Cu and Nb layers, were prepared by dc magnetron sputtering onto Si {100} wafers. The nominal total thickness of each layered film was 1 μm. The layer thickness was varied between 1 nm and 500 nm with the volume fraction of the two phases kept constant at 50%. The deposition rates and film densities were determined through a combination of profilometry and ion beam analysis techniques. Cross-sectional transmission electron microscopy (XTEM) was used to examine the structure, phase and grain size distribution of the as-sputtered films. A JEOL 3000F high resolution TEM was used to characterize the microstructure.

Experimental study of heat transfer in the boundary layer of a flat plate with the impact of weak shock waves on the leading edge

2020 ◽  
Author(s):  
V. L. Kocharin ◽  
A. A. Yatskikh ◽  
D. S. Prishchepova ◽  
A. V. Panina ◽  
Yu. G. Yermolaev ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Experimental Study ◽  
Shock Waves ◽  
Flat Plate ◽  
Leading Edge ◽  
Weak Shock ◽  
The Impact

scholarly journals Quantitative Experimental and Theoretical Investigations on the Interaction of Shock Waves with Magnetic Fields

1969 ◽  
Vol 24 (10) ◽  
pp. 1449-1457
Author(s):  
H. Klingenberg ◽  
F. Sardei ◽  
W. Zimmermann
Keyword(s):  
Magnetic Fields ◽  
Shock Waves ◽  
Physical Model ◽  
Spectroscopic Method ◽  
Experimental Results ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Theoretical Investigations ◽  
Theoretical Predictions ◽  
Interaction Of Shock Waves

Abstract In continuation of the work on interaction between shock waves and magnetic fields 1,2 the experiments reported here measured the atomic and electron densities in the interaction region by means of an interferometric and a spectroscopic method. The transient atomic density was also calculated using a one-dimensional theory based on the work of Johnson3 , but modified to give an improved physical model. The experimental results were compared with the theoretical predictions.

scholarly journals Modeling of Bridging Law for Bundled Aramid Fiber-Reinforced Cementitious Composite and its Adaptability in Crack Width Evaluation

Materials ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 179
Author(s):  
Daiki Sunaga ◽  
Takumi Koba ◽  
Toshiyuki Kanakubo
Keyword(s):  
Fiber Orientation ◽  
Crack Width ◽  
Volume Fraction ◽  
Characteristic Point ◽  
Crack Opening ◽  
Aramid Fiber ◽  
Cementitious Composite ◽  
Fiber Reinforced ◽  
Cross Sectional ◽  
Bridging Law

Tensile performance of fiber-reinforced cementitious composite (FRCC) after first cracking is characterized by fiber-bridging stress–crack width relationships called bridging law. The bridging law can be calculated by an integral calculus of forces carried by individual fibers, considering the fiber orientation. The objective of this study was to propose a simplified model of bridging law for bundled aramid fiber, considering fiber orientation for the practical use. By using the pullout characteristic of bundled aramid fiber obtained in the previous study, the bridging laws were calculated for various cases of fiber orientation. The calculated results were expressed by a bilinear model, and each characteristic point is expressed by the function of fiber-orientation intensity. After that, uniaxial tension tests of steel reinforced aramid-FRCC prism specimens were conducted to obtain the crack-opening behavior and confirm the adaptability of the modeled bridging laws in crack-width evaluation. The experimental parameters are cross-sectional dimensions of specimens and volume fraction of fiber. The test results are compared with the theoretical curves calculated by using the modeled bridging law and show good agreements in each parameter.

Mechanical thumb pain in a systemic sclerosis patient: simple first carpometacarpal osteoarthritis?

Rheumatology ◽  
2021 ◽  
Author(s):  
Guillaume LARID ◽  
Pier-Olivier DUBOE ◽  
Jean-Denis LAREDO ◽  
Elisabeth GERVAIS
Keyword(s):  
Systemic Sclerosis ◽  
Signal Intensity ◽  
Topoisomerase I ◽  
Joint Space ◽  
Carpometacarpal Joint ◽  
Cross Sectional ◽  
First Carpometacarpal Joint ◽  
Provide Pain Relief ◽  
Long Time ◽  
Carpometacarpal Osteoarthritis

Abstract A 70-year-old female patient treated with methotrexate for diffuse cutaneous systemic sclerosis (SSc) came up with mechanical pain over the left thumb for several months. SSc was diagnosed based on a clinical picture associating puffy fingers, skin sclerosis, wrist arthralgia, pulmonary hypertension, presence of antinuclear factors and antibodies against Topoisomerase-I. Her complaint was attributed to first carpometacarpal joint osteoarthritis and treated with orthesis, which did not provide pain relief after 5 months of regular use. Hand radiograph showed first carpometacarpal arthropathy with joint space narrowing and marked sclerosis of the first proximal metacarpal (A). MRI showed an area of very low signal intensity on T1- and T2-weighted images (B) within the proximal metacarpal, distal trapezium and medial joint recess surrounded by bone marrow edema. Mild peripheral enhancement was present after gadolinium injection. CT-scan (C) showed that the low signal intensity material visible at MRI consisted of calcium. These aspects are suggestive of scleroderma arthropathy rather than common first carpometacarpal osteoarthritis. Though involvement of the first carpometacarpal joint is long time known in SSc [1], it remains exceptional when looking at cross-sectional studies [2]. Carefully analyzing imaging exams is the key point in order not to miss this rare scleroderma feature.

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