scholarly journals Variability of the adiabatic parameter in monoatomic thermal and non-thermal plasmas

2018 ◽  
Vol 616 ◽  
pp. A58 ◽  
Author(s):  
Miguel A. de Avillez ◽  
Gervásio J. Anela ◽  
Dieter Breitschwerdt
Keyword(s):  
Internal Energy ◽  
Impact Ionization ◽  
Thermal Evolution ◽  
Numerical Models ◽  
Linear Equations ◽  
Thermal Plasmas ◽  
Specific Heats ◽  
Partial Pivoting ◽  
Electron Distributions ◽  
Collisional Ionization

Context. Numerical models of the evolution of interstellar and integalactic plasmas often assume that the adiabatic parameter γ (the ratio of the specific heats) is constant (5/3 in monoatomic plasmas). However, γ is determined by the total internal energy of the plasma, which depends on the ionic and excitation state of the plasma. Hence, the adiabatic parameter may not be constant across the range of temperatures available in the interstellar medium. Aims. We aim to carry out detailed simulations of the thermal evolution of plasmas with Maxwell–Boltzmann and non-thermal (κ and n) electron distributions in order to determine the temperature variability of the total internal energy and of the adiabatic parameter. Methods. The plasma, composed of H, He, C, N, O, Ne, Mg, Si, S, and Fe atoms and ions, evolves under collisional ionization equilibrium conditions, from an initial temperature of 109 K. The calculations include electron impact ionization, radiative and dielectronic recombinations and line excitation. The ionization structure was calculated solving a system of 112 linear equations using the Gauss elimination method with scaled partial pivoting. Numerical integrations used in the calculation of ionization and excitation rates are carried out using the double-exponential over a semi-finite interval method. In both methods a precision of 10−15 is adopted. Results. The total internal energy of the plasma is mainly dominated by the ionization energy for temperatures lower than 8 × 104 K with the excitation energy having a contribution of less than one percent. In thermal and non-thermal plasmas composed of H, He, and metals, the adiabatic parameter evolution is determined by the H and He ionizations leading to a profile in general having three transitions. However, for κ distributed plasmas these three transitions are not observed for κ < 15 and for κ < 5 there are no transitions. In general, γ varies from 1.01 to 5/3. Lookup tables of the γ parameter are presented as supplementary material.

scholarly journals Thermo-Viscoelastic Modeling of the Aircraft Tire Cornering

2015 ◽  
Vol 1099 ◽  
pp. 80-86 ◽  
Author(s):  
Iulian Rosu ◽  
Lama Elias-Birembaux ◽  
Frederic Lebon
Keyword(s):  
Thermal Evolution ◽  
Numerical Models ◽  
Frictional Heating ◽  
Mechanical Analysis ◽  
High Speeds ◽  
Numerical Studies ◽  
Deformation Dynamics ◽  
Viscoelastic Modeling ◽  
Fully Coupled ◽  
Tread Rubber

Some numerical models are proposed for simulate the aircraft tire behaviour on the ground in critical situations. Fully coupled thermo-mechanical analysis procedures taking into account finite deformation, dynamics and frictional contact are studied; the visco-elasticity properties of the rubber were identified. A good agreement is observed at moderate speed, thus the model is extrapolated to high speeds and seems able to predict results in cases for which it is not possible to obtain realistic experimental data. In order to understand the thermal evolution of tire tread rubber materials during rolling and skidding steps, new experimental and numerical studies were also realized on tire tread rubber. The aim of this approach is to simulate and understand the effect of frictional heating on the tire behaviour.

scholarly journals VII. On the ratio of the specific heats of the paraffins and their monohalogen derivatives

1894 ◽  
Vol 54 (326-330) ◽  
pp. 101-105
Keyword(s):  
Internal Energy ◽  
Specific Heats ◽  
Organic Gases

The experiments were undertaken to find whether the internal energy of the molecules of organic gases, as deduced from the ratio of the specific heats, showed any regularities corresponding to the chemical resemblances symbolised by the graphic formulæ. The paraffins and their monohalogen derivatives are very suitable for the purpose, as their chemical relations to each other are simple, they are easily volatile, and are stable enough to be unaffected by ordinary purifying agents.

Primary deformation phases during "magma-poor" rifting with special focus on the tectono-thermal evolution during the necking process

2020 ◽  
Author(s):  
Pauline Chenin ◽  
Gianreto Manatschal ◽  
Stefan M. Schmalholz ◽  
Thibault Duretz
Keyword(s):  
Lower Crust ◽  
Thermal Evolution ◽  
Numerical Models ◽  
Pure Shear ◽  
Geothermal Gradient ◽  
Special Focus ◽  
Distal Margin ◽  
Large Variability ◽  
Rifted Margins ◽  
Morphotectonic Evolution

&lt;p&gt;Although so-called &quot;magma-poor&quot; rifted margins display a large variability on a local scale, they are characterized by a number of common primary features worldwide such as their first-order architecture (proximal, necking, hyperextended, exhumation and oceanic domains), their lithological evolution along dip and the deformation processes associated with their different rifting stages. In this contribution, we first emphasize the primary morphological and lithological architecture of magma-poor rifted margins and how they relate to specific deformation modes (pure shear thinning, mechanical necking, frictional extensional wedge, detachment faulting and seafloor spreading). Second, we focus on the necking stage of rifting, which corresponds to the first major thinning event (when the crust is thinned from its initial thickness to ~ 10 km). We display the range of possible topographic and thermal evolutions of &quot;magma-poor&quot; and &quot;sedimentary starved&quot; rift systems depending on their lithosphere rheology. Our two-dimensional thermo-mechanical numerical models suggest that extension of lithospheres where the crust and the mantle are mechanically decoupled by a weak lower crust results in a complex morphotectonic evolution of rift systems, with formation of temporary restricted sub-basins framed by uplifted parts of the future distal margin. Mechanical decoupling between the crust and the mantle controls also largely the thermal evolution of rift systems during the necking phase since for equivalent extension rates and initial geotherms: (i) weak/decoupled lithospheres have a higher geothermal gradient at the end of the necking phase than strong/coupled lithospheres; and (ii) weak/decoupled lithospheres show intense heating of the lower crust at the rift center and intense cooling of the crust on either side of the rift center, unlike strong/coupled lithospheres. These behaviors contrast with the continuous subsidence and cooling predicted by the commonly used depth-uniform thinning model.&lt;/p&gt;

scholarly journals Numerical Simulation of Full Carburizing Process of an Automotive Gear

2021 ◽  
Author(s):  
Patrice Lasne ◽  
Philippe Bristiel ◽  
Nicolas Poulain
Keyword(s):  
Thermal Stresses ◽  
Thermal Evolution ◽  
Numerical Models ◽  
Carbon Diffusion ◽  
Phase Changes ◽  
Chemical Compositions ◽  
Relative Contribution ◽  
Temperature Boundary ◽  
Transformation Diagrams ◽  
Carburizing Process

Abstract The objective of the paper is to present material and numerical models needed to simulate with accuracy the full carburizing process of an automotive gear. The rough dimensions of the gear studied are 120mm in diameter and 45mm in height. From a numerical standpoint, as the carburizing affects only a thin layer under the surface, the mesh discretization must be adapted. Consequently, anisotropic mesh is used to describe accurately this zone. The temporal discretization must be also adapted to follow carbon diffusion and thermal evolution. The material models represent metallurgical phenomena during the complete carburizing process. The initial heating of the part induces phases transformation due to austenization. Subsequently, while holding at carburizing temperature, boundary conditions are applied to diffuse carbon into the part. While carbon content increases next to the surface, austenitic metallurgical grain growth is also modelled. A final cooling sets the properties of the carburized part. The model takes into account the phase changes using phase transformation diagrams locally adapted to chemical compositions and grain sizes. Simulation is used to predict the in-use properties of the gear at the end of the carburizing process as well as important results such as assessment of distortion and residual stresses. Thermal stresses, volume variation due to phase changes, and transformation plasticity all contribute to establish the final mechanical properties of the part. During the complete process, the material is modelled with an elasto-viscoplastic behavior and mixing methods are used to consider the relative contribution of each phase.

Shock waves in a gas with several relaxing internal energy modes

1965 ◽  
Vol 21 (4) ◽  
pp. 591-610 ◽  
Author(s):  
John F. Clarke ◽  
J. B. Rodgers
Keyword(s):  
Shock Waves ◽  
Velocity Profile ◽  
Internal Energy ◽  
Local Equilibrium ◽  
Relaxation Times ◽  
Internal Mode ◽  
Specific Heats ◽  
Transport Effects ◽  
Mode Energy ◽  
Steady Shock

The structure of plane steady shock waves in a gas with several internal energy modes which relax in parallel is investigated. Transport effects are neglected. Conditions for continuity and monotonicity of the velocity profile are discussed; when all modes have constant specific heats and relaxation times it is established that velocity must decrease monotonically. Internal mode energy contents may overshoot their local equilibrium values.Numerical results for waves in a hypothetical gas with two relaxing modes are presented for purposes of illustration.

scholarly journals A mushy Earth's mantle for more than 500 Myr after the magma ocean solidification

2020 ◽  
Vol 221 (2) ◽  
pp. 1165-1181
Author(s):  
J Monteux ◽  
D Andrault ◽  
M Guitreau ◽  
H Samuel ◽  
S Demouchy
Keyword(s):  
Thermal Evolution ◽  
Numerical Models ◽  
Spherical Geometry ◽  
Magma Ocean ◽  
Mantle Dynamics ◽  
Mineral Physics ◽  
The Earth ◽  
Complete Melting ◽  
Metal Silicate ◽  
Impact Heating

SUMMARY In its early evolution, the Earth mantle likely experienced several episodes of complete melting enhanced by giant impact heating, short-lived radionuclides heating and viscous dissipation during the metal/silicate separation. After a first stage of rapid and significant crystallization (Magma Ocean stage), the mantle cooling is slowed down due to the rheological transition, which occurs at a critical melt fraction of 40–50%. This transition first occurs in the lowermost mantle, before the mushy zone migrates toward the Earth's surface with further mantle cooling. Thick thermal boundary layers form above and below this reservoir. We have developed numerical models to monitor the thermal evolution of a cooling and crystallizing deep mushy mantle. For this purpose, we use a 1-D approach in spherical geometry accounting for turbulent convective heat transfer and integrating recent and solid experimental constraints from mineral physics. Our results show that the last stages of the mushy mantle solidification occur in two separate mantle layers. The lifetime and depth of each layer are strongly dependent on the considered viscosity model and in particular on the viscosity contrast between the solid upper and lower mantle. In any case, the full solidification should occur at the Hadean–Eoarchean boundary 500–800 Myr after Earth's formation. The persistence of molten reservoirs during the Hadean may favor the absence of early reliefs at that time and maintain isolation of the early crust from the underlying mantle dynamics.

Analog and digital simulations of Maxwellian plasmas forastrophysics

2008 ◽  
Vol 86 (1) ◽  
pp. 209-216 ◽  
Author(s):  
D W Savin ◽  
N R Badnell ◽  
P Beiersdorfer ◽  
B R Beck ◽  
G V Brown ◽  
...  
Keyword(s):  
Electron Impact ◽  
Impact Ionization ◽  
Ion Trap ◽  
Dielectronic Recombination ◽  
Impact Excitation ◽  
Electron Impact Excitation ◽  
Atomic Data ◽  
Fractional Abundance ◽  
Collisional Ionization ◽  
Ionization Balance

Many astrophysical and laboratory plasmas possess Maxwell–Boltzmann (MB) electron energy distributions (EEDs). Interpreting or predicting the properties of these plasmas requires accurate knowledge of atomic processes such as radiative lifetimes, electron impact excitation and de-excitation, electron impact ionization, radiative recombination, dielectronic recombination, and charge transfer, all for thousands of levels or more. Plasma models cannot include all of the needed levels and atomic data. Hence, approximations need to be made to make the models tractable. Here we report on an “analog” technique we have developed for simulating a Maxwellian EED using an electron beam ion trap and review some recent results using this method. A subset of the atomic data needed for modeling Maxwellian plasmas relates to calculating the ionization balance. Accurate fractional abundance calculations for the different ionization stages of the various elements in the plasma are needed to reliably interpret or predict the properties of the gas. However, much of the atomic data needed for these calculations have not been generated using modern theoretical methods and are often highly suspect. Here we will also review our recent updating of the recommended atomic data for “digital’ computer simulations of MB plasmas in collisional ionization equilibrium (CIE), describe the changes relative to previously recommended CIE calculations, and discuss what further recombination and ionization data are needed to improve this latest set of recommended CIE calculations. PACS Nos.: 34.70.+e,34.80.Dp, 34.80.Kw, 34,80,Lx, 52.50.–j, 52.20.Fs, 52.20.Hv, 52.25.Jm, 52,72.+v, 52.75.–d, 95.30.Dr, 95.30.Ky, 98.38.Bn, 98.58.Bz

scholarly journals Thermal Effects at Continent-Ocean Transform Margins: A 3D Perspective

Geosciences ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 193
Author(s):  
Daniel W. Schmid ◽  
Karthik Iyer ◽  
Ebbe H. Hartz
Keyword(s):  
Thermal Evolution ◽  
Numerical Models ◽  
Source Rocks ◽  
3D Fem ◽  
Boundary Segment ◽  
Continental Area ◽  
Transform Margin ◽  
Spreading Rates ◽  
A Minor ◽  
The Impact

Continental breakup along transform margins produces a sequence of (1) continent-continent, (2) continent-oceanic, (3) continent-ridge, and (4) continent-oceanic juxtapositions. Spreading ridges are the main sources of heat, which is then distributed by diffusion and advection. Previous work focused on the thermal evolution of transform margins built on 2D numerical models. Here we use a 3D FEM model to obtain the first order evolution of temperature, uplift/subsidence, and thermal maturity of potential source rocks. Snapshots for all four transform phases are provided by 2D sections across the margin. Our 3D approach yields thermal values that lie in between the previously established 2D end-member models. Additionally, the 3D model shows heat transfer into the continental lithosphere across the transform margin during the continental-continental transform stage ignored in previous studies. The largest values for all investigated quantities in the continental area are found along the transform segment between the two ridges, with the maximum values occurring near the transform-ridge corner of the trailing continental edge. This boundary segment records the maximum thermal effect up to 100 km distance from the transform. We also compare the impact of spreading rates on the thermal distribution within the lithosphere. The extent of the perturbation into the continental areas is reduced in the faster models due to the reduced exposure times. The overall pattern is similar and the maximum values next to the transform margin is essentially unchanged. Varying material properties in the upper crust of the continental areas has only a minor influence.

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