scholarly journals Erratum: Dynamics of Dusty Vortices I: Extensions and limitations of the terminal velocity approximation

2020 ◽  
Vol 496 (2) ◽  
pp. 2230-2230
Author(s):  
Francesco Lovascio ◽  
Sijme-Jan Paardekooper
Keyword(s):  
Terminal Velocity ◽  
Velocity Approximation

scholarly journals Dynamics of dusty vortices – I. Extensions and limitations of the terminal velocity approximation

2019 ◽  
Vol 488 (4) ◽  
pp. 5290-5299 ◽  
Author(s):  
Francesco Lovascio ◽  
Sijme-Jan Paardekooper
Keyword(s):  
Fluid Model ◽  
Velocity Model ◽  
Terminal Velocity ◽  
Viscous Stress Tensor ◽  
Spatial Convergence ◽  
Two Fluid Model ◽  
Numerical Solver ◽  
The Stability ◽  
Velocity Approximation ◽  
Protoplanetary Discs

ABSTRACT Motivated by the stability of dust laden vortices, in this paper we study the terminal velocity approximation equations for a gas coupled to a pressureless dust fluid and present a numerical solver for the equations embedded in the FARGO3D hydrodynamics code. We show that for protoplanetary discs it is possible to use the barycentre velocity in the viscous stress tensor, making it trivial to simulate viscous dusty protoplanetary discs with this model. We also show that the terminal velocity model breaks down around shocks, becoming incompatible with the two-fluid model it is derived from. Finally we produce a set of test cases for numerical schemes and demonstrate the performance of our code on these tests. Our implementation embedded in FARGO3D using an unconditionally stable explicit integrator is fast, and exhibits the desired second-order spatial convergence for smooth problems.

scholarly journals Polydisperse streaming instability – I. Tightly coupled particles and the terminal velocity approximation

2020 ◽  
Vol 499 (3) ◽  
pp. 4223-4238
Author(s):  
Sijme-Jan Paardekooper ◽  
Colin P McNally ◽  
Francesco Lovascio
Keyword(s):  
Growth Rates ◽  
Time Scale ◽  
Stokes Number ◽  
Terminal Velocity ◽  
Streaming Instability ◽  
Dust Size Distribution ◽  
Dynamical Time ◽  
Tightly Coupled ◽  
Dust Component ◽  
Velocity Approximation

ABSTRACT We introduce a polydisperse version of the streaming instability (SI), where the dust component is treated as a continuum of sizes. We show that its behaviour is remarkably different from the monodisperse SI. We focus on tightly coupled particles in the terminal velocity approximation and show that unstable modes that grow exponentially on a dynamical time-scale exist. However, for dust to gas ratios much smaller than unity, they are confined to radial wavenumbers that are a factor $\sim 1/{\overline{\rm St}}$ larger than where the monodisperse SI growth rates peak. Here ${\overline{\rm St}}\ll 1$ is a suitable average Stokes number for the dust size distribution. For dust to gas ratios larger than unity, polydisperse modes that grow on a dynamical time-scale are found as well, similar as for the monodisperse SI and at similarly large wavenumbers. At smaller wavenumbers, where the classical monodisperse SI shows secular growth, no growing polydisperse modes are found under the terminal velocity approximation. Outside the region of validity for the terminal velocity approximation, we have found unstable epicyclic modes that grow on ∼104 dynamical time-scales.

Particle motion with air resistance

2012 ◽  
Vol 8 (1) ◽  
pp. 1-15
Author(s):  
Gy. Sitkei
Keyword(s):  
Basic Equation ◽  
Initial Conditions ◽  
Equation Of Motion ◽  
Terminal Velocity ◽  
Dimensionless Form ◽  
Wood Industry ◽  
Acceptable Error ◽  
General Validity ◽  
Practical Applications ◽  
Air Resistance

Motion of particles with air resistance (e.g. horizontal and inclined throwing) plays an important role in many technological processes in agriculture, wood industry and several other fields. Although, the basic equation of motion of this problem is well known, however, the solutions for practical applications are not sufficient. In this article working diagrams were developed for quick estimation of the throwing distance and the terminal velocity. Approximate solution procedures are presented in closed form with acceptable error. The working diagrams provide with arbitrary initial conditions in dimensionless form of general validity.

scholarly journals SAO 244567 (HEN1357): A Post-Agb Star which has turned into a Planetary Nebula within the last 20 years

1998 ◽  
Vol 11 (1) ◽  
pp. 358-358
Author(s):  
M. Parthasarathy
Keyword(s):  
Planetary Nebula ◽  
Far Infrared ◽  
Central Star ◽  
Terminal Velocity ◽  
Galactic Latitude ◽  
Iras Source ◽  
High Galactic Latitude ◽  
Alpha Emission ◽  
Early Type Star ◽  
Emission Strength

SAO 244567 (Henl357) (IRAS 17119-5926) is a high galactic latitude (1 = 331°, b = −12°) early type star, originally classified as a B or A type H-alpha emission line star by Henize (1976). It is an IRAS source with far infrared colours similar to planetary nebulae. The IUE ultraviolet spectra obtained during the last eight years show that the central star is rapidly evolving. It is found that the central star of this young PN has faded by a factor of 3 within the last seven eight years. The terminal velocity of the stellar wind has decreased from −3500 km/sec in 1988 to almost zero in 1994. In 1988 the C IV (1550A) line which was a P-Cygni profile with strong absorption component had almost vanished by 1994. The CIII] 1909A emission strength increased markedly within 4 years from 1988 to 1992. The optical spectra obtained since 1990 shows very clearly only the nebular spectrum which is very similar to that of low excitation planetary nebula. The optical spectrum of SAO 244567 obtained in 1971 shows that it was a post-AGB B 1 or B2 supergiant at that time. This result shows that SAO 244567 has turned into a planetary nebula within the last 20 years. Recently Bobrowsky (1994) obtained narrowband optically resolved images in both H-beta and [OIII] 5007A with the HST planetary camera which revealed a well resolved nebula of size 2 seconds of arc. In this paper we discuss the recent new results.

scholarly journals Analysis of the Physical Properties of Seeds of Selected Viburnum Species for the Needs of Seed Sorting Operations

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 711
Author(s):  
Zdzisław Kaliniewicz ◽  
Dariusz J. Choszcz
Keyword(s):  
Physical Properties ◽  
Ornamental Plants ◽  
Seed Mass ◽  
Terminal Velocity ◽  
Landscape Design ◽  
Physical Parameters ◽  
Regression Analyses ◽  
Uniform Size ◽  
Size Fractions ◽  
Physical Attributes

Viburnum is a genus of colorful and ornamental plants popular in landscape design on account of their high esthetic appeal. The physical properties of viburnum seeds have not been investigated in the literature to date. Therefore, the aim of this study was to characterize the seeds of selected Viburnum species and to search for potential relationships between their physical attributes for the needs of seed sorting operations. The basic physical parameters of the seeds of six Viburnum species were measured, and the relationships between these attributes were determined in correlation and regression analyses. The average values of the evaluated parameters were determined in the following range: terminal velocity—from 5.6 to 7.9 m s−1, thickness—from 1.39 to 1.87 mm, width—from 3.59 to 6.33 mm, length—from 5.58 to 7.44 mm, angle of external friction—from 36.7 to 43.8°, mass—from 16.7 to 35.0 mg. The seeds of V. dasyanthum, V. lentago and V. sargentii should be sorted in air separators, and the seeds of V. lantana and V. opulus should be processed with the use of mesh screens with round apertures to obtain uniform size fractions. The seeds of V. rhytodophyllum cannot be effectively sorted into batches with uniform seed mass, but they can be separated into groups with similar dimensions.

scholarly journals Ball sealer tracking and seating of temporary plugging fracturing technology in the perforated casing of a horizontal well

2021 ◽  
pp. 014459872110204
Author(s):  
Wan Cheng ◽  
Chunhua Lu ◽  
Guanxiong Feng ◽  
Bo Xiao
Keyword(s):  
Critical Parameter ◽  
Fluid Velocity ◽  
Stable State ◽  
Horizontal Wells ◽  
Terminal Velocity ◽  
Injection Rate ◽  
Fracturing Fluid ◽  
Perforation Hole ◽  
Horizontal Wellbore ◽  
Tight Reservoirs

Multistaged temporary plugging fracturing in horizontal wells is an emerging technology to promote uniform fracture propagation in tight reservoirs by injecting ball sealers to plug higher-flux perforations. The seating mechanism and transportation of ball sealers remain poorly understood. In this paper, the sensitivities of the ball sealer density, casing injection rate and perforation angle to the seating behaviors are studied. In a vertical wellbore section, a ball sealer accelerates very fast at the beginning of the dropping and reaches a stable state within a few seconds. The terminal velocity of a non-buoyant ball is greater than the fluid velocity, while the terminal velocity of a buoyant ball is less than the fluid velocity. In the horizontal wellbore section, the terminal velocity of a non-buoyant or buoyant ball is less than the fracturing fluid flowing velocity. The ball sealer density is a more critical parameter than the casing injection rate when a ball sealer diverts to a perforation hole. The casing injection rate is a more critical parameter than the ball sealer density when a ball sealer seats on a perforation hole. A buoyant ball sealer associated with a high injection rate of fracturing fluid is highly recommended to improve the seating efficiency.

scholarly journals The Ballistic Particle Model

1983 ◽  
Vol 100 ◽  
pp. 133-134
Author(s):  
Frank N. Bash
Keyword(s):  
Radial Velocity ◽  
Gravitational Potential ◽  
Molecular Clouds ◽  
Milky Way ◽  
Terminal Velocity ◽  
Particle Model ◽  
The Sun ◽  
Giant Molecular Clouds ◽  
Spiral Pattern ◽  
Armed Spiral

Bash and Peters (1976) suggested that giant molecular clouds (GMC's) can be viewed as ballistic particles launched from the two-armed spiral-shock (TASS) wave with orbits influenced only by the overall galactic gravitational potential perturbed by the spiral gravitational potential in the arms. For GMC's in the Milky Way, the model predicts that the radial velocity observed from the Sun increases with age (time since launch). We showed that the terminal velocity of CO observed from l ≃ 30° to l ≃ 60° can be understood if all GMC's are born in the spiral pattern given by Yuan (1969) and live 30 × 106 yrs. Older GMC's were predicted to have radial velocities which exceed observed terminal velocities.

An improved formula for terminal velocity of rigid spheres

1997 ◽  
Vol 50 (1-2) ◽  
pp. 53-61 ◽  
Author(s):  
A.V. Nguyen ◽  
H. Stechemesser ◽  
G. Zobel ◽  
H.J. Schulze
Keyword(s):  
Terminal Velocity ◽  
Rigid Spheres

Dynamic Crack Propagation in Single-Crystalline Silicon

1998 ◽  
Vol 539 ◽  
Author(s):  
T. Cramer ◽  
A. Wanner ◽  
P. Gumbsch
Keyword(s):  
Crack Propagation ◽  
Crystalline Silicon ◽  
Potential Drop ◽  
Tensile Tests ◽  
Terminal Velocity ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Single Crystalline Silicon ◽  
Single Crystalline ◽  
Crack Propagation Velocity

AbstractTensile tests on notched plates of single-crystalline silicon were carried out at high overloads. Cracks were forced to propagate on {110} planes in a <110> direction. The dynamics of the fracture process was measured using the potential drop technique and correlated with the fracture surface morphology. Crack propagation velocity did not exceed a terminal velocity of v = 3800 m/s, which corresponds to 83%7 of the Rayleigh wave velocity vR. Specimens fractured at low stresses exhibited crystallographic cleavage whereas a transition from mirror-like smooth regions to rougher hackle zones was observed in case of the specimens fractured at high stresses. Inspection of the mirror zone at high magnification revealed a deviation of the {110} plane onto {111} crystallographic facets.

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