Improvements to the RADIOM non-LTE model

In 1993, we proposed the RADIOM model [M. Busquet, Phys. Fluids 85 (1993) 4191] where an ionization temperature T_z is used to derive non-LTE properties from LTE data. T_z is obtained from an “extended Saha equation” where unbalanced transitions, like radiative decay, give the non-LTE behavior. Since then, major improvements have been made. T_z has been shown to be more than a heuristic value, but describes the actual distribution of excited and ionized states and can be understood as an “effective temperature”. Therefore we complement the extended Saha equation by introducing explicitly the auto-ionization/dielectronic capture. Also we use the SCROLL model to benchmark the computed values of T_z.     

The penny-shaped crack at a bonded plane with localized elastic non-homogeneity

This paper examines the axisymmetric problem pertaining to a penny-shaped crack which is located at the bonded plane of two similar elastic halfspace regions which exhibit localized axial variations in the linear elastic shear modulus, which has the form G(z)=G₁+G₂e^±ζz. The equations of elasticity governing this type of non-homogeneity are solved by employing a Hankel transform technique. The resulting mixed boundary value problem associated with the penny-shaped crack is reduced to a Fredholm integral equation of the second kind which is solved in a numerical fashion to generate the crack opening mode stress intensity factor at the tip.     

On the accuracy of finite element and finite difference predictions of non-newtonian slot pressures for a maxwell fluid

Plane slow flow of a Maxwell fluid over a transverse slot is considered. Results are computed by a finite difference method (FDM) using the differential form of the constitutive equation, and by a finite element method (FEM) using the integral form. Even on fine grids, the two methods produce different results, particularly at low D_e. However, extrapolation of the results of zero mesh spacing shows excellent agreement between the two methods. Hence both methods are convergent with mesh refinement, but high accuracy would require extremely fine meshes. An explanation is provided for why it is unreasonable to expect either method accurately to obtain the singular limit of P_e/N₁ as D_e → 0. Also an explanation for the errors at very low D_e is offered. If we presume the second-order fluid (SOE) result holds for very low D_e (ie. P_e = N₁/4), both the FEM and FDM predict only minor deviation from this value for the Maxwell fluid, in the range 0 ⩽ D_e ⩽ 1.     

Determination of current flow in a plasma by a simulation method

A method is proposed which, for specific assumptions, allows us to determine the density distribution of a constant current flowing between electrodes in a plasma for plane parallel or radially symmetric electric and magnetic fields, allowing for anisotropic conductivity.Notation e_r, e, e_z unit vectors in a cylindrical coordinate system - E, e_r, e_z electric field strength vector and its components - V electric field potential - H, H_r, H, H_z magnetic field strength and its components - j current density vector - e electron charge - m electron mass - c velocity of light - momentum transfer time - ₀ normal plasma conductivity - _e electron cyclotron frequency - h unit vector in the direction of the magnetic field     

The near wake of sinusoidal wavy cylinders: Three-dimensional POD analyses

Three-dimensional (3D) proper orthogonal decomposition (POD) analyses are conducted to investigate the near wake of sinusoidal wavy cylinders. For a wave amplitude a/D_m = 0.152, three typical spanwise wavelengths (λ_z) of the wavy cylinder are taken into account, i.e., λ_z/D_m = 1.89, 3.79 and 6.06, where D_m is the mean diameter of the wavy cylinder, among which λ_z/D_m = 1.89 and 6.06 are the optimum wavelengths corresponding to the largest reduction/suppression of fluid forces acting on the wavy cylinder. Time- and space-resolved three-component velocities of the near wake flow, obtained from large eddy simulation (LES) at a subcritical Reynolds number Re = 3 × 10³, are used in the 3D POD analyses. Comparison is made among the wavy cylinders of the three λ_z/D_m values as well as between them and a smooth cylinder, in terms of POD modes, mode energy, mode coefficients, as well as reconstructed flow structures by lower modes. For the optimum λ_z/D_m = 1.89 and 6.06, energy associated with the first two POD modes is significantly reduced compared with that for λ_z/D_m = 3.79 and the smooth cylinder. Distinct characteristics are observed on the lower POD modes for the wavy cylinders. It is found that the first two POD modes for λ_z/D_m = 1.89 and 6.06 are linked to large-scale streamwise vortices that are additionally introduced into the near wake due to the wavy geometry. Meanwhile, POD mode 3 suggests that the wavy cylinder with the larger optimum λ_z/D_m (= 6.06) generates dominant hairpin-like and spanwise coherent structures (CSs) shedding from the saddle at a different frequency from those shedding from the node. Evolutionary development of these CSs is discussed based on reconstructed flows.     

An experimental platform for creating white dwarf photospheres in the laboratory

We present an experimental platform for measuring hydrogen Balmer emission and absorption line profiles for plasmas with white dwarf (WD) photospheric conditions (T_e ～1 eV, n_e ～10¹⁷ cm^?3). These profiles will be used to benchmark WD atmosphere models, which, used with the spectroscopic method, are responsible for determining fundamental parameters (e.g., effective temperature, mass) for tens of thousands of WDs. Our experiment, performed at the Z Pulsed Power Facility at Sandia National Laboratories, uses the large amount of X-rays generated from a z-pinch dynamic hohlraum to drive plasma formation in a gas cell. The platform is unique compared to past hydrogen line profile experiments in that the plasma is radiation-driven. This decouples the heating source from the plasma to be studied in the sense that the radiation temperature causing the photoionization is independent of the initial conditions of the gas. For the first time we measure hydrogen Balmer lines in absorption at these conditions in the laboratory for the purpose of benchmarking Stark-broadened line shapes. The platform can be used to study other plasma species and to explore non-LTE, time-dependent collisional-radiative atomic kinetics.     

Heat Convection of Compressible Viscous Fluids: I

The stationary problem for the heat convection of compressible fluid is considered around the equilibrium solution with the external forces in the horizontal strip domain z ₀ < z < z ₀ + 1 and it is proved that the solution exists uniformly with respect to z ₀ ≥ Z ₀. The limit system as z ₀ → + ∞ is the Oberbeck–Boussinesq equations.     

Basic equations for the microscopic theory of plasticity of polycrystalline materials with given texture

An expression for the yield stress of anisotropic materials is applied to the anisotropic strength of hard rolled copper foils whose crystallographic texture is known. We assume that this crystallographic texture is the only cause of the anisotropic plastic behaviour of the material. The model used for the yield stress is also used to deduce:

1. Stress-strain relations for isotropic polycrystalline materials;
2. A formula for the fully plastic strain tensor, applied to anisotropic hard rolled copper foils.

For the anisotropic copper foils considered the calculated curves of the yield stress and of the strain tensor as a function of the angle x between rolling and tensile direction agree qualitatively with the measured values. However, the theory is not complete, since the yield stress and the plastic strain tensor are both a function of a parameter Q, the fraction of the number of available crystallographic slip planes on which the maximum shear stress has reached the critical value τ_a. We assume that for “fully” plastic deformation a certain critical fraction Q _e of the total number of slip planes has to be active. The fraction Q _e is called the critical active quantity. With the parameter Q _e we adjust the calculated curves to the measured ones. The dependence of Q _e on the properties of the material (e.g. the crystallographic texture) is discussed in Appendix I.     

Inverse Estimation of the Effective Diffusion of the Filter in the In Situ Diffusion and Retention (DR) Experiment

Porous filters are often used in laboratory and in situ diffusion and retention experiments. The proper interpretation of these experiments requires knowing the effective diffusion, D _e, of the filter which is commonly determined from laboratory diffusion experiments or estimated from the filter porosity. The D _e of the filter in the in situ experiment may differ from the D _e of the filter measured in the laboratory due to pore clogging. Here, we present an inverse method to estimate the D _e of the filter of in situ diffusion experiments. The method has been tested for several sampling schemes, numbers of synthetic data, N, and standard deviations of the noise, ??. It has been applied to the following tracers used in the in situ diffusion and retention (DR) experiment performed in the Opalinus clay at Mont Terri underground research laboratory: HTO/HDO, Br^?,I^?, ²² Na⁺,¹³³ Ba²⁺,⁸⁵ Sr²⁺, Cs⁺/¹³⁷Cs⁺, and ⁶⁰Co²⁺. The estimation error increases with the standard deviation of the noise of the data and decreases with the number of data. It is smallest for sorbing tracers. The D _e of the filter can be properly estimated from 12 data collected within the first 3?days for conservative tracers as long as ????? 0.02 and for sorbing tracers as long as ??????0.05. The estimate of D _e for conservative tracers is poor when data are collected from a 10-day experiment with daily sampling. The convergence of the estimation algorithm for conservative tracers improves by starting with a value of the D _e smaller than the true value. The choice of the initial value of D _e does not affect the convergence of the estimation algorithm for sorbing tracers. Filter clogging and vertical flow though the filter can influence the tracer transport through the filter. The use of the D _e of the filter obtained from a laboratory test for the in situ experiment may result in large errors for strongly sorbing tracers. Such errors can be overcome by estimating the equivalent D _e of the filter with the proposed inverse method which will be useful for the design of in situ diffusion experiments.     

Deformational behaviour of a polymeric particle layer

Deformational behaviour of viscoelastic particulate materials in uniaxial compression, at constant temperature, has been studied on powdered PVC. It has been shown that both creep deformation and creep recovery of a PVC particle layer at constant temperature can be described by the equationΦ = A e ^BP t^z whereΦ is porosity,P pressure,t time andA, B andz are constants. For a narrow pressure range the relationshipz = CP applies whereC is a constant dependent onB.     

The comparison model method: A new arithmetic approach to the discrete inverse problem of groundwater hydrology

Let the steady-state pressure z(·) of a fluid in a one-dimensional domain be governed by the equation d _x (a d _x z) = f subject to Dirichlet boundary conditions. We consider the identification of the transmissivity a (·), given f(·), and measured pressure z(·) by the comparison model method, a direct method which has been known and applied for some time but lacked theoretical background. With reference to a domain in one spatial dimension, we examine both the infinite-(‘continuous’) and finite-(discrete) dimensional cases. In the former, the method is based on the solution p(·) of an auxiliary flow equation, where f(·) and the two-point boundary conditions are unchanged with respect to the original or z(·) equation, whereas a tentative constant value b is assigned to the auxiliary transmissivity. The ratio of the first derivatives of p(·) and z(·) multiplied by b yields a solution ã(·) to the inverse problem. We examine in detail the nonuniqueness of ã(·) as a function of b, some cases where existence implies uniqueness, the role of positivity constraints, and a special feature: self-identifiability. We then translate all available results into the discrete case, where the good unknowns for the inverse problem are the internode coefficients. Several algebraic and numerical examples are presented.     

Evaluation of the Spectral Element Dynamic Model for Large-Eddy Simulation on Unstructured,Deformed Meshes

In this paper, the Spectral-Element Dynamic Model (SEDM), suited for Large-Eddy Simulation (LES) using Discontinuous Finite Element Methods (DFEM), is assessed using unstructured meshes. Five test cases of increasing complexity are considered, namely, the Taylor-Green vortex at Re =?5000, the turbulent channel flow at Re_τ =?587, the circular cylinder in cross-flow at Re_D =?3900, the square cylinder in cross-flow at Re_D =?22400 and the channel with periodic constrictions at Re_h =?10595. Various discretization parameters such as the grid spacing, polynomial degree and numerical flux are assessed and very accurate results are reported in all cases. This consistency in the results demonstrates the versatility of the SEDM approach and its ability to gage the actual resolution and quality of the mesh and, accordingly, to introduce an amount of sub-grid dissipation which is adapted to the spatial discretization considered.     

A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAs under general thermomechanical loading conditions

We present a fully general, three dimensional, constitutive model for Shape Memory Alloys (SMAs), aimed at describing all of the salient features of SMA evolutionary response under complex thermomechanical loading conditions. In this, we utilize the mathematical formulation we have constructed, along with a single set of the model’s material parameters, to demonstrate the capturing of numerous responses that are experimentally observed in the available SMA literature. This includes uniaxial, multi-axial, proportional, non-proportional, monotonic, cyclic, as well as other complex thermomechanical loading conditions, in conjunction with a wide range of temperature variations. The success of the presented model is mainly attributed to the following two main factors. First, we use multiple inelastic mechanisms to organize the exchange between the energy stored and energy dissipated during the deformation history. Second, we adhere strictly to the well established mathematical and thermodynamical requirements of convexity, associativity, normality, etc. in formulating the evolution equations governing the model behavior, written in terms of the generalized internal stress/strain tensorial variables associated with the individual inelastic mechanisms. This has led to two important advantages: (a) it directly enabled us to obtain the limiting/critical transformation surfaces in the spaces of both stress and strain, as importantly required in capturing SMA behavior; (b) as a byproduct, this also led, naturally, to the exhibition of the apparent deviation from normality, when the transformation strain rate vectors are plotted together with the surfaces in the space of external/global stresses, that has been demonstrated in some recent multi-axial, non-proportional experiments.     

Pressure-Gradient Turbulent Boundary Layers Developing Around a Wing Section

A direct numerical simulation database of the flow around a NACA4412 wing section at R e _c = 400,000 and 5^° angle of attack (Hosseini et al. Int. J. Heat Fluid Flow 61, 117–128, 2016), obtained with the spectral-element code Nek5000, is analyzed. The Clauser pressure-gradient parameter β ranges from ? 0 and 85 on the suction side, and from 0 to ? 0.25 on the pressure side of the wing. The maximum R e _?? and R e _τ values are around 2,800 and 373 on the suction side, respectively, whereas on the pressure side these values are 818 and 346. Comparisons between the suction side with zero-pressure-gradient turbulent boundary layer data show larger values of the shape factor and a lower skin friction, both connected with the fact that the adverse pressure gradient present on the suction side of the wing increases the wall-normal convection. The adverse-pressure-gradient boundary layer also exhibits a more prominent wake region, the development of an outer peak in the Reynolds-stress tensor components, and increased production and dissipation across the boundary layer. All these effects are connected with the fact that the large-scale motions of the flow become relatively more intense due to the adverse pressure gradient, as apparent from spanwise premultiplied power-spectral density maps. The emergence of an outer spectral peak is observed at β values of around 4 for λ _z ? 0.65δ ₉₉, closer to the wall than the spectral outer peak observed in zero-pressure-gradient turbulent boundary layers at higher R e _?? . The effect of the slight favorable pressure gradient present on the pressure side of the wing is opposite the one of the adverse pressure gradient, leading to less energetic outer-layer structures.