Probing of laser-irradiated solid targets using coherent extreme ultra-violet radiation

The diagnostic potential of extreme ultraviolet (EUV) coherent probing within a laser produced plasma is investigated. A fluid code is used to model the interaction of a 35 fs, 2 × 10¹⁴ Wcm^?2 800 nm laser pulse with an 800 nm thick aluminium target. A post processor is used to calculate the refractive index and transmission to 45 eV radiation of the target. The effects of EUV radial phase variations at the rear of the target on the intensity distribution at a detector 1.5 m from the target are studied. An irradiated aluminium target is found to have little effect on the transmission of 45 eV radiation, however, there are significant phase retardation differences of the probing beam in the radial direction. These phase variations affect the subsequent propagation of the radiation, suggesting that a simple diagnostic that measures the far-field footprint of the coherent EUV radiation passing through an irradiated target is sensitive to radial variations of the target heating. Sample calculated footprint variations associated with a drop in laser absorption to an irradiance of 10¹⁴ Wcm^?2 at a radius from the focal centre of 50 μm are shown.     

Simulations of hot, dense iron plasma opacity at 89 eV and comparison with experiment

Predictions of hot, dense iron plasma opacity at 89 eV photon energy are compared with experimental determinations from the transmission of laser-heated iron to extreme ultra-violet (EUV) laser radiation. The EUV laser was pumped using six beams of an Nd-Yag laser in a refraction compensating geometry, while another beam irradiated a tamped solid iron target with an intensity of 10¹⁴ W cm⁻². The Ehybrid hydrodynamic and atomic physics code was used to predict temperatures, densities and ionisation throughout the evolving iron plasma. The iron opacities were deduced taking into account free–free, bound–free and bound–bound absorption. Bound–bound absorption was considered using atomic data generated by the Opacity Project. Reasonable overall agreement between theory and experiment was obtained for the iron layer transmission. The simulations indicated the dominance of bound–bound absorption throughout most regions of the iron plasma, but also the potential importance of photoionisation from core levels where energetically possible.     

Effect of the surface thermal radiation on turbulent natural convection in tall cavities of façade elements

The effect of the surface thermal radiation in tall cavities with turbulent natural convection regime was analyzed and quantified numerically. The parameters considered were: the Rayleigh number 10⁹–10¹², the aspect ratio 20, 40 and 80 and the emmisivity 0.0–1.0. The percentage contribution of the radiative surface to the total heat transfer has a maximum value of  15.19% (Ra = 10⁹, A = 20) with emissivity equal to 1.0 and a minimum of 0.5% (Ra = 10¹², A = 80) with ε* = 0.2. The average radiative Nusselt number for a fixed emissivity is independent of the Rayleigh number, but for a fixed Rayleigh number diminishes with the increase of the aspect ratio. The results indicate that the surface thermal radiation does not modify significantly the flow pattern in the cavity, just negligible effects in the bottom and top of the cavity were observed. Two different temperature patterns were observed a conductive regime Ra = 10⁹ and a boundary layer regime Ra = 10¹².     

Stability, Instability, and Error of the Force-based Quasicontinuum Approximation

Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are popular tools in computational physics. For example, the force-based quasicontinuum (QCF) approximation is the only known pointwise consistent quasicontinuum approximation for coupling a general atomistic model with a finite element continuum model. In this paper, we present a detailed stability and error analysis of this method. Our optimal order error estimates provide a theoretical justification for the high accuracy of the QCF approximation: they clearly demonstrate that the computational efficiency of continuum modeling can be utilized without a significant loss of accuracy if defects are captured in the atomistic region. The main challenge we need to overcome is the fact that the linearized QCF operator is typically not positive definite. Moreover, we prove that no uniform inf-sup stability condition holds for discrete versions of the W ^1,p -W ^1,q “duality pairing” with 1/p + 1/q = 1, if 1 ≤ p < ∞. However, we were able to establish an inf-sup stability condition for a discrete version of the W ^1,∞-W ^1,1 “duality pairing” which leads to optimal order error estimates in a discrete W ^1,∞-norm.     

Two-fluid modeling of Geldart A particles in gas-fluidized beds

We have investigated the effect of cohesion and drag models on the bed hydrodynamics of Geldart A particles based on the two-fluid （TF） model. For a high gas velocity U0 = 0.03 m/s, we found a transition from the homogeneous fluidization to bubbling fluidization with an increase of the coefficient C1, which is used to account for the contribution of cohesion to the excess compressibility. Thus cohesion can play a role in the bed expansion of Geldart A particles. Apart from cohesion, we have also investigated the influence of the drag models. When using the Wen and Yu drag correlation with an exponent n = 4.65, we find an under-prediction of the bed expansion at low gas velocities （U0 = 0.009 m/s）. When using a larger exponent （n = 9.6）, as reported in experimental studies of gas-fluidization, a much better agreement with the experimental bed expansion is obtained. These findings suggest that at low gas velocity, a scale-down of the commonly used drag model is required. On the other hand, a scale-up of the commonly used drag model is necessary at high gas velocity （U0 = 0.2 and 0.06 m/s）. We therefore conclude that scaling the drag force represent only an ad hoc way of repairing the deficiencies of the TF model, and that a far more detailed study is required into the origin of the failure of the TF model for simulating fluidized beds of fine powders.     

Intense ultrashort laser–Xe cluster interaction

The last several years have witnessed a surge of activity involving the interaction of clusters with intense ultrashort pulse lasers. The interest in laser–cluster interaction has not been only of academic interest, but also because of the wide variety of potential applications. Clusters can be used as a compact source of X-rays, incoherent as well as coherent, and of fast ions capable of driving a fusion reaction in deuterium plasmas. In one set of xenon cluster experiments, in particular, amplification of ～2.8 Å X-rays has been observed [28]. X-ray amplification in cluster media is a phenomenon of critical importance and may lead to applications such as EUV lithography, EUV and X-ray microscopy, X-ray tomography, and variety of applications in biology and material sciences. However, while amplification of ～2.8 Å X-rays has been documented in experiments, the mechanism for producing it remains to be fully understood. In this talk, a xenon model of laser–cluster interaction dynamics is presented to shed light on the processes responsible for amplification. The focus of this research is on the feasibility of creating population inversions and gain in some of the inner-shell hole state transitions within the M-shell of highly ionized xenon. The model couples a molecular dynamics (MD) treatment of the explosively-driven, non-Maxwellian cluster expansion to a comprehensive multiphoton-radiative ionization dynamic (ID) model including single- and double-hole state production within the Co- and Fe-like ionization stages of xenon. The hole-state dynamics is self-consistently coupled to a detailed valence-state collisional-radiative dynamics of the Ni-, Co-, and Fe-like ionization stages of xenon. In addition, the model includes tunneling ionization rates that confirm an initial condition assumption that Ni-like ground states can be created almost instantaneously, on the order of a femtosecond or less, i.e., at laser intensities larger than 10¹⁹ W/cm², all of the N-shell, n = 4 electrons are striped from a xenon atom in less than a femtosecond. Because of the abundance of these ground states, large numbers of n = 2, inner-shell hole states and large population inversions can be created when the Ni-like ground states are photo- or collisionally ionized. Once the M-shell is entered, tunneling ionization slows down as does collisional ionization due to the fall in ion density as the cluster expands. Moreover, as the cluster density goes down, our combined MD and ID calculations show that so do the calculated population inversions. Thus, our calculations do not support the initial experimental data interpretations in which the measured gains have been associated with double holes in more highly ionized stages of xenon (Xe³²⁺, Xe³⁴⁺, Xe³⁵⁺, and Xe³⁷⁺), which our calculations suggest would require laser intensities in excess of 1.5 × 10²⁰ W/cm², for a 248 nm, ～250 fs laser pulse focused in a gas of xenon clusters. At laser intensities used in the experiment, such ionization stages would be reached, but only later in time when cluster densities have fallen by several orders of magnitude from their initial values to values where pumping rates are too low and gains cannot be generated.     

Nonlinear Effects in Osmotic Volume Flows of Electrolyte Solutions through Double-Membrane System

The results of experimental study of volume osmotic flows in a double-membrane system are presented in this article. The double-membrane system consists of two membranes (M _u, M _d) oriented in horizontal planes and three identical compartments (u, m, d), containing unstirred binary or ternary ionic solutions. In this system concentrations of the solutions fulfil the following conditions C _us  = C _ds  < C _ms (s = 1 or 2). Solutions of aqueous potassium chloride or ammonia were used as binary solutions, whereas potassium chloride dissolved in aqueous ammonia solution or ammonia dissolved in aqueous potassium chloride solution were used as ternary solutions. For binary solutions, the dependencies of a volume flux (J _v) on potassium chloride or ammonia concentration (C _ms ) are linear, whereas for ternary solutions these dependencies are nonlinear. The volume flux amplification and the osmotic conductivity coefficients were calculated on the basis of experimental data. The coefficient of the volume flux amplification for ternary solutions in comparison to binary ones depends on solutes concentrations and has maximum values dependent on solutes concentrations. Similarly, the osmotic conductivity coefficient has maximal values dependent on solutes concentrations. Moreover, the thermodynamic model of the osmotic volume flux was developed and the results were interpreted within the gravitational instability category.     

Corrections to statistical modeling of spectra for plasmas at moderate or low temperatures

For plasmas in LTE at moderate or low temperatures (1–50 eV), the statistical approach for calculating emission or absorption spectra may become inaccurate and need improvement to account for the Boltzmann factor in the population of the levels. In this work, corrections to the transition rates are computed by using the moments of emission or absorption zones, which represent the set of levels within a configuration that provide the dominant part of the emissivity (or opacity). Partition functions are also improved by using high-order moments of level energy distributions. Corrections to the statistical models are derived in a non-relativistic framework as a function of these moments, which can be deduced from already published formulas. Numerical comparisons of detailed line-by-line and statistical calculations are presented that clearly illustrate the importance of correcting the models at low temperatures. Thus, these corrections are of great interest for applications such as Warm Dense Matter, LTE photo-absorption experiments where the targets are heated to ∼T_e = 20 eV and astrophysical plasmas.     

Two-Phase Flow in Porous Media: Predicting Its Dependence on Capillary Number and Viscosity Ratio

Motivated by the need to determine the dependencies of two-phase flow in a wide range of applications from carbon dioxide sequestration to enhanced oil recovery, we have developed a standard two-dimensional, pore-level model of immiscible drainage, incorporating viscous and capillary effects. This model has been validated through comparison with several experiments. For a range of stable viscosity ratios (M = μ _injected,nwf/μ _{defending, wf} ≥ 1), we had increased the capillary number, N _c and studied the way in which the flows deviate from fractal capillary fingering at a characteristic time and become compact for realistic capillary numbers. This crossover has enabled predictions for the dependence of the flow behavior upon capillary number and viscosity ratio. Our results for the crossover agreed with earlier theoretical predictions, including the universality of the leading power-law indicating its independence of details of the porous medium structure. In this article, we have observed a similar crossover from initial fractal viscous fingering (FVF) to compact flow, for large capillary numbers and unstable viscosity ratios M < 1. In this case, we increased the viscosity ratio from infinitesimal values, and studied the way in which the flows deviate from FVF at a characteristic time and become compact for non-zero viscosity ratios. This crossover has been studied using both our pore-level model and micro-fluidic flow-cell experiments. The same characteristic time, τ = 1/M ^0.7, satisfactorily describes both the pore-level results for a range of large capillary numbers and the micro-fluidic flow cell results. This crossover should lead to predictions similar to those mentioned above.     

Edge dislocations generated from a microcrack under initial residual stress of non-uniform distribution

Crystal nucleation gives rise to inhomogeneity in the crystal lattice. The prevailing stresses and strains caused by non-uniform cooling can create microcracks with residual stresses locked-in at the end segments. These stresses can have a non-uniform distribution where the amplitude can increase or decrease from the microcrack tip which is highly strained to generate edge dislocations under in-plane shear. A dual scale microdislocation crack model is considered by focusing attention near the microcrack tip singularity such that more than 10 orders of magnitude in lineal dimension can be covered from the atomic to the microscopic scale. The concept of a scale multiplier is employed to connect the microscopic and atomic scale results. Discontinuity at the cross-scaling location is necessitated by dividing the full range of the non-equilibrium process into two regions within which equilibrium mechanics can be used. When needed, additional mesoregions can be added to reduce the transient discontinuities.Solved in closed form is the solution for the generation of edge dislocations due to non-uniform residual stress distributions at the end segment of the microcrack tip which will henceforth be referred to simply as the “tip”. Three different Cases I, II and III will be considered where the residual stress will possess a peak at the different locations. Case I for the furthest away from the tip, Case II for the peak nearest to the tip and Case III for the peak in the middle of the residual stress segment. Compared are the scale multiplier α whose maximum value being one corresponding to no discontinuity at cross-scaling. Hence, small α corresponds to large discontinuity. For Cases I, II and III, αs are found, respectively as 0.17, 0.43 and 0.28. The largest discontinuity occurred at α = 0.17 when the peak of the residual stress is farthest away from the microcrack tip. The largest number of edge dislocations or imperfections are also generated for Case I. The precise location of the residual stress peak is related to the magnitude and the segment length of the residual stress. These findings are manifestation of the variety of non-homogeneities that can arise in a metal alloy during crystal formation, not to mention the prevailing conditions at the grain boundaries. The idea is not to account for the details per se but to test the sensitivities of the microscopic and atomic parameters involved. To this end, the energy density function for the dual scale model will be determined and discussed in connection with what has been emphasized.     

Unique Solutions to Hartree–Fock Equations for Closed Shell Atoms

In this paper we study the problem of uniqueness of solutions to the Hartree and Hartree–Fock equations of atoms. We show, for example, that the Hartree–Fock ground state of a closed shell atom is unique provided the atomic number Z is sufficiently large compared to the number N of electrons. More specifically, a two-electron atom with atomic number Z\geqq 35{Z\geqq 35} has a unique Hartree–Fock ground state given by two orbitals with opposite spins and identical spatial wave functions. This statement is wrong for some Z > 1, which exhibits a phase segregation.     

Critical datasets for benchmarking atomic codes: Calibrated line intensities emitted by well-diagnosed solar plasmas

The accuracy of available spectral codes is dependent on the quality of the atomic data and transition rates that they include, and can only be tested by benchmarking predicted line emissivities with observations from plasmas whose physical properties are known with precision. In the present work we describe a few high-resolution spectra emitted by solar flare plasmas under condition of ionization equilibrium, and one quiet Sun off-disk region spectrum, and we propose these datasets as benchmarks for the assessment of the accuracy of existing spectral codes in the 1.84–1.90 Å and 3.17–3.22 Å X-ray ranges and in the 500–1600 Å far ultraviolet range.     

Micro/macro-crack growth due to creep–fatigue dependency on time–temperature material behavior

The implicit character of micro-structural degradation is determined by specifying the time history of crack growth caused by creep–fatigue interaction at high temperature. A dual scale micro/macro-equivalent crack growth model is used to illustrate the underlying principle of multiscaling which can be applied equally well to nano/micro. A series of dual scale models can be connected to formulate triple or quadruple scale models. Temperature and time-dependent thermo-mechanical material properties are developed to dictate the design time history of creep–fatigue cracking that can serve as the master curve for health monitoring.In contrast to the conventional procedure of problem/solution approach by specifying the time- and temperature-dependent material properties as a priori, the desired solution is then defined for a class of anticipated loadings. A scheme for matching the loading history with the damage evolution is then obtained. The results depend on the initial crack size and the extent of creep in proportion to fatigue damage. The path dependent nature of damage is demonstrated by showing the range of the pertinent parameters that control the final destruction of the material. A possible scenario of 20 yr of life span for the 38Cr2Mo2VA ultra-high strength steel is used to develop the evolution of the micro-structural degradation. Three micro/macro-parameters μ^*, d^* and σ^* are used to exhibit the time-dependent variation of the material, geometry and load effects. They are necessary to reflect the scale transitory behavior of creep–fatigue damage. Once the algorithm is developed, the material can be tailor made to match the behavior. That is a different life span of the same material would alter the time behavior of μ^*, d^* and σ^* and hence the micro-structural degradation history. The one-to-one correspondence of the material micro-structure degradation history with that of damage by cracking is the essence of path dependency. Numerical results and graphs are obtained to demonstrate how the inherently implicit material micro-structure parameters can be evaluated from the uniaxial bulk material properties at the macroscopic scale.The combined behavior of creep and fatigue can be exhibited by specifying the parameter ξ with reference to the initial defect size a₀. Large ξ (0.90 and 0.85) gives critical crack size a_cr = 11–14 mm (at t < 20 yr) for a₀ about 1.3 mm. For small ξ (0.05 and 0.15), there results critical a_cr = 6–7 mm (at t < 20 yr) for a₀ about 0.7–0.8 mm. The initial crack is estimated to increase its length by an order of magnitude before triggering global to the instability. This also applies ξ ≈ 0.5 where creep interacts severely with fatigue. Fine tuning of a_cr and a₀ can be made to meet the condition oft = 20 yr.Trade off among load, material and geometric parameters are quantified such that the optimum conditions can be determined for the desired life qualified by the initial–final defect sizes. The scenario assumed in this work is indicative of the capability of the methodology. The initial–final defect sizes can be varied by re-designing the time–temperature material specifications. To reiterate, the uniqueness of solution requires the end result to match with the initial conditions for a given problem. This basic requirement has been accomplished by the dual scale micro/macro-crack growth model for creep and fatigue.     

Development and characterization of a variable turbulence generation system

Experimental turbulent combustion studies require systems that can simulate the turbulence intensities [u′/U ₀ ~ 20–30% (Koutmos and McGuirk in Exp Fluids 7(5):344–354, 1989)] and operating conditions of real systems. Furthermore, it is important to have systems where turbulence intensity can be varied independently of mean flow velocity, as quantities such as turbulent flame speed and turbulent flame brush thickness exhibit complex and not yet fully understood dependencies upon both U ₀ and u′. Finally, high pressure operation in a highly pre-heated environment requires systems that can be sealed, withstand high gas temperatures, and have remotely variable turbulence intensity that does not require system shut down and disassembly. This paper describes the development and characterization of a variable turbulence generation system for turbulent combustion studies. The system is capable of a wide range of turbulence intensities (10–30%) and turbulent Reynolds numbers (140–2,200) over a range of flow velocities. An important aspect of this system is the ability to vary the turbulence intensity remotely, without changing the mean flow velocity. This system is similar to the turbulence generators described by Videto and Santavicca (Combust Sci Technol 76(1):159–164, 1991) and Coppola and Gomez (Exp Therm Fluid Sci 33(7):1037–1048, 2009), where variable blockage ratio slots are located upstream of a contoured nozzle. Vortical structures from the slots impinge on the walls of the contoured nozzle to produce fine-scale turbulence. The flow field was characterized for two nozzle diameters using three-component Laser Doppler velocimetry (LDV) and hotwire anemometry for mean flow velocities from 4 to 50 m/s. This paper describes the key design features of the system, as well as the variation of mean and RMS velocity, integral length scales, and spectra with nozzle diameter, flow velocity, and turbulence generator blockage ratio.     

Contribution to the Modelling of Coupled Heat and Mass Transfers on 3D Real Structure of Heterogeneous Building Materials: Application to Hemp Concrete

Hydraulic flow, electrical flow and the passage of elastic waves through porous media are all linked by electrokinetic processes. In its simplest form, the passage of elastic waves through the porous medium causes fluid to flow through that medium and that flow gives rise to an electrical streaming potential and electrical counter-current. These processes are frequency-dependent and governed by coupling coefficients which are themselves frequency-dependent. The link between fluid pressure and fluid flow is described by dynamic permeability, which is characterised by the hydraulic coupling coefficient (C_hp). The link between fluid pressure and electrical streaming potential is characterised by the streaming potential coefficient (C_sp). While the steady-state values of such coefficients are well studied and understood, their frequency dependence is not. Previous work has been confined to unconsolidated and disaggregated materials such as sands, gravels and soils. In this work, we present an apparatus for measuring the hydraulic and streaming potential coefficients of high porosity, high permeability consolidated porous media as a function of frequency. The apparatus operates in the range 1 Hz to 2 kHz with a sample of 10 mm diameter and 5–30 mm in length. The full design and validation of the apparatus are described together with the experimental protocol it uses. Initial data are presented for three samples of Boise sandstone, which present as dispersive media with the critical transition frequency of 918.3?±?99.4 Hz. The in-phase and in-quadrature components of the measured hydraulic and streaming potential coefficients have been compared to the Debye-type dispersion model as well as theoretical models based on bundles of capillary tubes and porous media. Initial results indicate that the dynamic permeability data present an extremely good fit to the capillary bundle and Debye-type dispersion models, while the streaming potential coefficient presents an extremely good fit to all of the models up to the critical transition frequency, but diverges at higher frequencies. The streaming potential coefficient data are best fitted by the Pride model and its Walker and Glover simplification. Characteristic pore size values calculated from the measured critical transition frequency fell within 1.73% of independent measures of this parameter, while the values calculated directly from the Packard model showed an underestimation by about 12%.

     

Unsteady flow and heat transfer analysis of an impinging synthetic jet

The present paper focuses on the analysis of unsteady flow and heat transfer regarding an axisymmetric impinging synthetic jet on a constant heat flux disc. Synthetic jet is a zero net mass flux jet that provides an unsteady flow without any external source of fluid. Present results are validated against the available experimental data showing that the SST/k − ω turbulence model is more accurate and reliable than the standard and low-Re k − ε models for predicting heat transfer from an impinging synthetic jet. It is found that the time-averaged Nusselt number enhances as the nozzle-to-plate distance is increased. As the oscillation frequency in the range of 16–400 Hz is increased, the heat transfer is enhanced. It is shown that the instantaneous Nu distribution along the wall is influenced mainly by the interaction of produced vortex ring and wall boundary layer. Also, the fluctuation level of Nu decreases as the frequency is raised.     

A numerical study of non-isothermal turbulent coaxial jets

In this work, we propose to study non isothermal air–air coaxial jets with two different approaches: parabolic and elliptic approaches. The standard k−ε model and the RSM model were applied in this study. The numerical resolution of the equations governing this flow type was carried out for: the parabolic approach, by a “home-made” CFD code based on a finite difference method, and the elliptic approach by an industrial code (FLUENT) based on a finite volume method. In forced convection mode (Fr = ∞), the two turbulence models are valid for the prediction of the mean flow. But for turbulent sizes, k−ε model gives results closer to those achieved in experiments compared to RSM Model. Concerning the limit of validity of the parabolic and elliptic approaches, we showed that for velocities ratio r lower than 1, the results of the two approaches were satisfactory. On the other hand, for r > 1, the difference between the results became increasingly significant. In mixed convection mode (Fr ≅ 20), the results obtained by the two turbulence models for the mean axial velocity were very different even in the plume region. For the temperature and the turbulent sizes the two models give satisfactory results which agree well with the correlations suggested by the experimenters for X ≥ 20. Thus, the second order model with σ _t = 0.85 is more effective for a coaxial jet study in a mixed convection mode.