Comparison Between Exact and One-Dimensional Theories for Incipient Melting in Reentry Simulation

1966 ◽  
Vol 88 (4) ◽  
pp. 428-434 ◽  
Author(s):  
Richard A. Matula
Keyword(s):  
Temperature Distribution ◽  
Transient Temperature ◽  
Stagnation Temperature ◽  
Free Flight ◽  
Dimensional Solution ◽  
Radial Temperature ◽  
One Dimensional ◽  
Flight Range ◽  
Wide Range ◽  
The One

The exact transient temperature distribution in a spherical region subjected to an axisymmetric reentry heat flux has been evaluated. The results are presented in terms of nondimensional parameters, therefore they are valid for a wide range of materials, flight conditions, and nose radii. The angular dependence of the surface temperature is given as a function of time. It is also shown that the true radial temperature distribution can be represented by an exponential function. Finally, the solution is applied to reentry ablation onset studies that are being conducted in the free-flight range of the GM Defense Research Laboratories. The exact solution and the one-dimensional theory for the stagnation temperature rise of a model simulating reentry conditions in the free-flight range are compared. It is shown that the validity of the one-dimensional solution is dependent on the flight time, material properties, and nose radius of the model. Assuming that a temperature can be assigned which corresponds to incipient ablation, the present analysis is particularly useful in the prediction of ablation onset.

scholarly journals Plane thermonuclear detonation waves initiated by proton beams and quasi-one-dimensional model of fast ignition

2014 ◽  
Vol 33 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Alexander A. Charakhch'yan ◽  
Konstantin V. Khishchenko
Keyword(s):  
Detonation Wave ◽  
Fusion Reaction ◽  
Plasma Heating ◽  
Symmetry Plane ◽  
Detonation Waves ◽  
Proton Beams ◽  
One Dimensional ◽  
Wide Range ◽  
The One ◽  
Α Particles

AbstractThe one-dimensional problem on bilatiral irradiation by proton beams of the plane layer of condensed DT mixture with length 2H and density ρ0 ≤ 100ρs, where ρs is the fuel solid-state density at atmospheric pressure and temperature of 4 K, is considered. The proton kinetic energy is 1 MeV, the beam intensity is 1019 W/cm2 and duration is 50 ps. A mathematical model is based on the one-fluid two-temperature hydrodynamics with a wide-range equation of state of the fuel, electron and ion heat conduction, DT fusion reaction kinetics, self-radiation of plasma and plasma heating by α-particles. If the ignition occurs, a plane detonation wave, which is adjacent to the front of the rarefaction wave, appears. Upon reflection of this detonation wave from the symmetry plane, the flow with the linear velocity profile along the spatial variable x and with a weak dependence of the thermodynamic functions of x occurs. An appropriate solution of the equations of hydrodynamics is found analytically up to an arbitrary constant, which can be chosen so that the analytical solution describes with good accuracy the numerical one. The gain with respect to the energy of neutrons G ≈ 200 at Hρ0 ≈ 1 g/cm2, and G > 2000 at Hρ0 ≈ 5 g/cm2. To evaluate the ignition energy Eig of cylindrical targets, the quasi-1D model, limiting trajectories of α-particles by a cylinder of a given radius, is suggested. The model reproduces the known theoretical dependence Eig ~ ρ0−2 and gives Eig = 160 kJ for ρ0 = 100ρs ≈ 22 g/cm3.

The Transient Temperature Distribution in a Slab Subject to Thermal Radiation

1965 ◽  
Vol 87 (1) ◽  
pp. 117-130 ◽  
Author(s):  
R. D. Zerkle ◽  
J. Edward Sunderland
Keyword(s):  
Temperature Distribution ◽  
Thermal Radiation ◽  
Radiant Heat ◽  
Analog Computer ◽  
Graphical Form ◽  
Transient Temperature ◽  
Transient Temperature Distribution ◽  
Temperature Distributions ◽  
Approximate Analytical Solutions ◽  
Wide Range

The transient, one-dimensional temperature distribution is determined for a slab, insulated on one face, and subjected to thermal radiation at the other face. The slab is initially at a uniform temperature and is assumed to be homogeneous, isotropic, and opaque; the physical properties are assumed to be independent of temperature. Transient temperature distributions for both heating and cooling situations are obtained by means of a thermal-electrical analog computer. A diode limiter circuit is used to simulate the nonlinear radiant heat flux. The transient temperature distributions are presented in a dimensionless, graphical form for a wide range of variables. Approximate analytical solutions are also given which complement and extend the solution charts over ranges of parameters not covered in the charts.

Study on the transient temperature distribution of new conical friction plate under sliding friction

2021 ◽  
pp. 095440702110696
Author(s):  
Yanzhong Wang ◽  
Peng Liu
Keyword(s):  
Temperature Distribution ◽  
Temperature Gradient ◽  
Temperature Rise ◽  
Friction Surface ◽  
Sliding Friction ◽  
Conical Surface ◽  
Transient Temperature ◽  
Radial Temperature Gradient ◽  
Radial Temperature ◽  
Friction Plate

Conical friction surface is a novel configuration for friction plate in transmission. Numerical FEA models for transient heat transfer and distribution of conically grooved friction plate have been established to investigate the thermal behavior of the conical surface with different configurations. The finite element method is used to obtain the numerical solution, the temperature test data of conical surface are obtained by the friction test rig. In order to study and compare the temperature behavior of conically grooved friction plate, several three-dimensional transient temperature models are established. The heat generated on the friction interface during the continuous sliding process is calculated. Two different pressure conditions were defined to evaluate the influence of different load conditions on temperature rise and the effects of conical configuration parameters on surface temperature distribution are investigated. The results show that the radial temperature gradient on conical friction surface is obvious. The uniform pressure condition could be used when evaluating the temperature rise of conically grooved friction plate. The increase of the cone height could improve the radial temperature gradient of the conically grooved friction plate.

scholarly journals THE ONE-DIMENSIONAL WAVE SPECTRA AT LIMITED FETCH

1972 ◽  
Vol 1 (13) ◽  
pp. 13
Author(s):  
Hisashi Mitsuyasu
Keyword(s):  
Similarity Theory ◽  
Wind Waves ◽  
Laboratory Data ◽  
Peak Frequency ◽  
Wave Spectra ◽  
One Dimensional ◽  
Wide Range ◽  
Laboratory Tank ◽  
The One ◽  
Dimensional Wave

The data for the spectra of wind-generated waves measured in a laboratory tank and in a bay are analyzed using the similarity theory of Kitaigorodski, and the one-dimensional spectra of fetch-limited wind waves are determined from the data. The combined field and laboratory data cover such a wide range of dimensionless fetch F (= gF/u2 ) as F : 102 ~ 10 . The fetch relations for the growthes of spectral peak frequency u)m and of total energy E of the spectrum are derived from the proposed spectra, which are consistent with those derived directly from the measured spectra.

scholarly journals Rare temperature histories and cirrus ice number density in a parcel and a one-dimensional model

2014 ◽  
Vol 14 (23) ◽  
pp. 13013-13022 ◽  
Author(s):  
D. M. Murphy
Keyword(s):  
Temperature Dependence ◽  
Low Temperatures ◽  
Ice Crystals ◽  
Strong Increase ◽  
Number Density ◽  
Dimensional Model ◽  
One Dimensional ◽  
Slow Growth Rate ◽  
Wide Range ◽  
The One

Abstract. A parcel and a one-dimensional model are used to investigate the temperature dependence of ice crystal number density. The number of ice crystals initially formed in a cold cirrus cloud is very sensitive to the nucleation mechanism and the detailed history of cooling rates during nucleation. A possible small spread in the homogeneous freezing threshold due to varying particle composition is identified as a sensitive nucleation parameter. In a parcel model, the slow growth rate of ice crystals at low temperatures inherently leads to a strong increase in ice number density at low temperatures. This temperature dependence is not observed. The model temperature dependence occurs for a wide range of assumptions and for either homogeneous or, less strongly, heterogeneous freezing. However, the parcel model also shows that random temperature fluctuations result in an extremely wide range of ice number densities. A one-dimensional model is used to show that the rare temperature trajectories resulting in the lowest number densities are disproportionately important. Low number density ice crystals sediment and influence a large volume of air. When such fall streaks are included, the ice number becomes less sensitive to the details of nucleation than it is in a parcel model. The one-dimensional simulations have a more realistic temperature dependence than the parcel mode. The one-dimensional model also produces layers with vertical dimensions of meters even if the temperature forcing has a much broader vertical wavelength. Unlike warm clouds, cirrus clouds are frequently surrounded by supersaturated air. Sedimentation through supersaturated air increases the importance of any process that produces small numbers of ice crystals. This paper emphasizes the relatively rare temperature trajectories that produce the fewest crystals. Other processes are heterogeneous nucleation, sedimentation from the very bottom of clouds, annealing of disordered to hexagonal ice, and entrainment.

First Paper: A General Approach to Hydraulic Lock

1967 ◽  
Vol 182 (1) ◽  
pp. 595-602 ◽  
Author(s):  
P. Dransfield ◽  
D. M. Bruce ◽  
M. Wadsworth
Keyword(s):  
Reynolds Equation ◽  
Lateral Force ◽  
Hydraulic Control ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Particular Solutions ◽  
Piston Cylinder ◽  
The One ◽  
Hydraulic Control System ◽  
General Method

The present state of knowledge on the hydraulic lock phenomena of oil hydraulic control system components is reviewed briefly. A general one-dimensional solution of the Reynolds equation which governs hydraulic lock is presented. The solution embraces the particular solutions of past workers, and allows ready solution for piston-cylinder configurations for which a one-dimensional solution is adequate. A general method for making full solutions of the Reynolds equation is presented, requiring the use of a digital computer for particular solutions. Pressure distribution, the lateral force on the piston which produces hydraulic lock, and the location of the lateral force can be obtained. The commonly occurring case of a single-land piston lying tilted in its bore is examined in detail. The limit of accuracy of a one-dimensional solution is clearly shown by illustrating the discrepancies between the one-dimensional and two-dimensional solutions for several configurations.

NUMERICAL STUDIES ON THE VIBRATIONAL SPECTRUM OF FIBONACCI CHAIN: A MULTIFRACTAL ANALYSIS

1991 ◽  
Vol 05 (05) ◽  
pp. 825-841 ◽  
Author(s):  
WLODZIMIERZ SALEJDA
Keyword(s):  
Vibrational Spectrum ◽  
Multifractal Analysis ◽  
Scaling Laws ◽  
Model Parameters ◽  
Local Scaling ◽  
One Dimensional ◽  
Dynamic Matrix ◽  
Numerical Studies ◽  
Wide Range ◽  
The One

A harmonic Hamiltonian modelling the lattice dynamics of the one-dimensional Fibonacci-type quasicrystal is studied numerically. The multifractal analysis of vibrational spectrum is performed. It is found that the integrated normalized density of states [Formula: see text], where x denotes the square of the eigenenergy of the dynamic matrix, exhibits a finite range of scaling indices α (i.e. α min ≤α≤ α max ) describing the local scaling laws of [Formula: see text]. The α-f spectra and the Renyi dimensions [Formula: see text] are calculated in a wide range of model parameters taking into account the next-nearest-neighbour (NNN) interactions of atoms. In particular, we have observed that: (1) The α-f spectra are smooth in the interval [Formula: see text]; (2) If the so-called parameter of quasi-periodicity Q increases, then αmin and the fractal dimension of vibrational spectra [Formula: see text] decrease; (3) If the strength of NNN interactions h grows then α min decreases but D increases.

Numerical and Analytical Solutions for Two-Dimensional Gas Distribution in Gas-Loaded Heat Pipes

1989 ◽  
Vol 111 (3) ◽  
pp. 598-604 ◽  
Author(s):  
P. F. Peterson ◽  
C. L. Tien
Keyword(s):  
Heat Pipes ◽  
Computational Effort ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Gas Distribution ◽  
Dimensional Solution ◽  
Integral Analysis ◽  
One Dimensional ◽  
Wide Range ◽  
Design Calculations

This work presents a two-dimensional axisymmetric diffusion model for the non-condensable gas distribution in gas-loaded heat pipes and thermosyphons. The new model, based on an integral analysis, has major advantages over existing, computationally time consuming, two-dimensional models. It has equal accuracy while using only the computational effort required for the cruder one-dimensional model, and also includes the effects of wall conduction and spatial variation of the condenser heat transfer coefficient. To simplify design calculations further an analytic two-dimensional solution is established, which gives excellent results over a wide range of parameters.

A Viscoelastic Model for the Dynamic Behavior of Saturated Poroelastic Soils

1992 ◽  
Vol 59 (1) ◽  
pp. 128-135 ◽  
Author(s):  
J. P. Bardet
Keyword(s):  
Elastic Moduli ◽  
Viscoelastic Model ◽  
Degree Of Saturation ◽  
Biot Theory ◽  
One Dimensional ◽  
Poroelastic Materials ◽  
Proposed Model ◽  
Wide Range ◽  
Dynamic Loadings ◽  
The One

A viscoelastic model is proposed to describe the dynamic response of the saturated poroelastic materials that obey the Biot theory (1956). The viscoelastic model is defined from the velocity and attenuation of dilatational and distortional waves in poroelastic materials. Its material properties are defined in terms of the elastic moduli, porosity, specific gravity, degree of saturation, and permeability of the soils. The proposed model is tested by comparing its response with the one of poroelastic materials in the case of axial and lateral harmonic loadings of one-dimensional columns. The viscoelastic model is simpler to use than poroelastic materials but yields similar results for a wide range of soils and dynamic loadings.

Supramolecular architectures in CoIIand CuIIcomplexes with thiophene-2-carboxylate and 2-amino-4,6-dimethoxypyrimidine ligands

2016 ◽  
Vol 72 (5) ◽  
pp. 442-450 ◽  
Author(s):  
Ammasai Karthikeyan ◽  
Packianathan Thomas Muthiah ◽  
Franc Perdih
Keyword(s):  
Hydrogen Bonds ◽  
Water Molecule ◽  
Coordination Polymers ◽  
Three Dimensional ◽  
Functional Materials ◽  
Supramolecular Architecture ◽  
Dinuclear Copper ◽  
One Dimensional ◽  
Wide Range ◽  
The One

The coordination chemistry of mixed-ligand complexes continues to be an active area of research since these compounds have a wide range of applications. Many coordination polymers and metal–organic framworks are emerging as novel functional materials. Aminopyrimidine and its derivatives are flexible ligands with versatile binding and coordination modes which have been proven to be useful in the construction of organic–inorganic hybrid materials and coordination polymers. Thiophenecarboxylic acid, its derivatives and their complexes exhibit pharmacological properties. Cobalt(II) and copper(II) complexes of thiophenecarboxylate have many biological applications, for example, as antifungal and antitumor agents. Two new cobalt(II) and copper(II) complexes incorporating thiophene-2-carboxylate (2-TPC) and 2-amino-4,6-dimethoxypyrimidine (OMP) ligands have been synthesized and characterized by X-ray diffraction studies, namely (2-amino-4,6-dimethoxypyrimidine-κN)aquachlorido(thiophene-2-carboxylato-κO)cobalt(II) monohydrate, [Co(C5H3O2S)Cl(C6H9N3O2)(H2O)]·H2O, (I), andcatena-poly[copper(II)-tetrakis(μ-thiophene-2-carboxylato-κ2O:O′)-copper(II)-(μ-2-amino-4,6-dimethoxypyrimidine-κ2N1:N3)], [Cu2(C5H3O2S)4(C6H9N3O2)]n, (II). In (I), the CoIIion has a distorted tetrahedral coordination environment involving one O atom from a monodentate 2-TPC ligand, one N atom from an OMP ligand, one chloride ligand and one O atom of a water molecule. An additional water molecule is present in the asymmetric unit. The amino group of the coordinated OMP molecule and the coordinated carboxylate O atom of the 2-TPC ligand form an interligand N—H...O hydrogen bond, generating anS(6) ring motif. The pyrimidine molecules also form a base pair [R22(8) motif]viaa pair of N—H...N hydrogen bonds. These interactions, together with O—H...O and O—H...Cl hydrogen bonds and π–π stacking interactions, generate a three-dimensional supramolecular architecture. The one-dimensional coordination polymer (II) contains the classical paddle-wheel [Cu2(CH3COO)4(H2O)2] unit, where each carboxylate group of four 2-TPC ligands bridges two square-pyramidally coordinated CuIIions and the apically coordinated OMP ligands bridge the dinuclear copper units. Each dinuclear copper unit has a crystallographic inversion centre, whereas the bridging OMP ligand has crystallographic twofold symmetry. The one-dimensional polymeric chains self-assembleviaN—H...O, π–π and C—H...π interactions, generating a three-dimensional supramolecular architecture.

Sign in / Sign up

Export Citation Format

Share Document