Two-dimensional Test Research Articles

Comparison of supersonic and subsonic expansion accelerations associated with fast magnetic reconnection

Supersonic and subsonic expansion acceleration mechanisms associated with spontaneous fast magnetic reconnection process are compared by two-dimensional magnetohydrodynamic (MHD) simulations and test fluid (non-charged) particle simulations. When the Petschek reconnection process is steadily established, the reconnection jet generated by a pair of slow shocks becomes either supersonic (Case 1) or subsonic (Case 2), depending on the upstream plasma condition. For Case 1, the jet generated by the slow shocks can be further accelerated by the adiabatic supersonic expansion process. Finally, the jet encounters a fast shock in front of the plasmoid. For Case 2, the jet generated by slow shocks can be further accelerated by the adiabatic subsonic expansion process. The acceleration of Case 1 is stronger than that of Case 2. In Case 2, a fast shock is not formed. In both cases, it is important that the propagation of the plasmoid is driven by slow shocks formed around the plasmoid itself, rather than the reconnection jet.

Effects of Blade Tip Clearances on the Suction-corner Performances of a High-load Axial Compressor Cascade

Strong adverse flows tend to occur in the suction surface/wall corner of high-load blade cascades of axial compressors. In a two-dimensional cascade wind tunnel test, effects of tip clearances on the cascade pressure coefficient Cp and flow structures in the corner were surveyed. Addition of a tip clearance was found to alter the flow conditions in the suction corner of axial compressor blade cascade. Tip clearance of 0.4 mm for the test blade of chord length of 100 mm in a typical high-load stator blade cascade increased the pressure coefficient Cp and lessened the corner loss coefficient compared with the cases with no clearance or with wider clearance. The issuing jet through the tip clearance of 0.4 mm was found to have eliminated strong vortices in the corner zone. It suggests a very useful means of improving the axial compressor performances.

Incorporation of Cabot's wall functions in RANS with applications in turbomachinery

Cabot's wall functions model (CWM) was originally introduced in conjunction with Large Eddy Simulations (LES), for modelling the turbulent near-wall flow. The present paper presents a novel application of CWM, namely its use within the framework of Reynolds Averaged Navier-Stokes (RANS) modelling. In the present work a q-ω turbulence model has been used. The implementation of the model has been validated considering five two-dimensional test cases including turbomachinery applications. The results confirm that CWM provides an advantageous approach also for RANS modelling, providing an optimal balance between accuracy and economy for modelling the near-wall turbulent flow. Compared to the low Reynolds number models (LRN), the CWM allows the use of a coarser grid near the wall, while providing better accuracy compared to the standard logarithmic wall-function methods. The applicability of a coarser near-wall resolution speeds up the simulation not only due to the reduced number of grid nodes, but also due to the fact that larger time-steps can be used without endangering the stability of the numerical solution. The computational results produced by CWM have been shown to either improve or retain the accuracy of the LRN model. Even in adverse pressure gradients, the model is observed to provide still a relatively good solution. Hence, CWM, with proper coding and suitable grids, has the potential providing solutions with comparable accuracy to LRN, while being much more economical.

Two‐dimensional, Time‐dependent, Multigroup, Multiangle Radiation Hydrodynamics Test Simulation in the Core‐Collapse Supernova Context

We have developed a time-dependent, multi-energy group, multiangle (Sn) Boltzmann transport scheme for radiation hydrodynamics simulations in one and two spatial dimensions. The implicit transport is coupled to both one-dimensional (spherically symmetric) and two-dimensional (axially symmetric) versions of the explicit Newtonian hydrodynamics code VULCAN. The two-dimensional variant, VULCAN/2D, can be operated in general structured or unstructured grids, and although the code can address many problems in astrophysics, it was constructed specifically to study the core-collapse supernova problem. Furthermore, VULCAN/2D can simulate the radiation hydrodynamic evolution of differentially rotating bodies. We summarize the equations solved and methods incorporated into the algorithm and present the results of a time-dependent two-dimensional test calculation. A more complete description of the algorithm is postponed to another paper. We highlight a two-dimensional test run that follows the immediate postbounce evolution of a collapsed core for 22 ms. We present the relationship between the anisotropies of the overturning matter field and the distribution of the corresponding flux vectors as a function of energy group. This is the first two-dimensional multigroup, multiangle, time-dependent radiation hydrodynamics calculation ever performed in core-collapse studies. Although the transport module of the code is not gray and does not use flux limiters (however, there is a flux-limited variant of VULCAN/2D), it still does not include energy redistribution and most velocity-dependent terms.

Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers.

A quantitative study is carried out in this paper to investigate the size of numerical viscosities and the resolution power of high-order weighted essentially nonoscillatory (WENO) schemes for solving one- and two-dimensional Navier-Stokes equations for compressible gas dynamics with high Reynolds numbers. A one-dimensional shock tube problem, a one-dimensional example with parameters motivated by supernova and laser experiments, and a two-dimensional Rayleigh-Taylor instability problem are used as numerical test problems. For the two-dimensional Rayleigh-Taylor instability problem, or similar problems with small-scale structures, the details of the small structures are determined by the physical viscosity (therefore, the Reynolds number) in the Navier-Stokes equations. Thus, to obtain faithful resolution to these small-scale structures, the numerical viscosity inherent in the scheme must be small enough so that the physical viscosity dominates. A careful mesh refinement study is performed to capture the threshold mesh for full resolution, for specific Reynolds numbers, when WENO schemes of different orders of accuracy are used. It is demonstrated that high-order WENO schemes are more CPU time efficient to reach the same resolution, both for the one-dimensional and two-dimensional test problems.

The Impact of Event Scale: Validation of an Italian version

Objective: To validate an Italian version of the Impact of Event Scale (IES) in patients addressing the emotional impact of a recent road accident. Methods: Seventy-nine subjects were examined within 1–34 weeks after an accident by means of (1) an Italian version of the IES, (2) a free description of the accident, and (3) a questionnaire assessing subjects' behaviour and feelings. Results: IES data were analysed by means of the principal component analysis (PCA) method, followed by a quartimax rotation, obtaining a two-factor solution interpreted as intrusion (Factor 1) and avoidance (Factor 2). Furthermore, the scores to the two subscales were considered in order to assess their predictive value on some variables linked to the traumatic event. Intrusion significantly discriminated the emotional intensity and fear level of subjects as a consequence of the accident. Conclusions: The IES is a two-dimensional test capable of evaluating posttraumatic stress. The intrusion and avoidance factors explained 40% of the total variance. The two-factor solution has a psychological counterpart and is similar to the findings of earlier studies conducted on a larger number of subjects in other countries.

Moisture structures of laterally expanding fingering flows in sandy soils

Water sometimes infiltrates into a sandy soil along preferential flow paths called fingers, rather than homogeneously. In order to understand the physical fundamentals of fingering flow, we carried out two-dimensional infiltration tests under continuous rainfall. Each finger was composed of two moisture structure zones, a finger core and a finger-swelling zone surrounding the finger core. Each finger can be classified as a low-swell finger (LSF) or a high-swell finger (HSF) based on the swelling velocity. In LSF, water moves laterally across a constant potential boundary where sorptivity is a dominant factor in making the finger swell. In HSF, on the other hand, water moves laterally through a constant flux boundary where pressure gradient is a driving force. In the latter, accordingly, the corresponding water flux can be estimated by the hydraulic conductivity multiplied by the water pressure gradient. Based on these observations, we propose a growth model for a finger moving downward along with subsequent lateral expansion, which makes it possible to estimate the area of soil wetted by fingers. The estimated area is in a fairly good agreement with that observed.

Core losses in claw pole permanent magnet machines with soft magnetic composite stators

This paper presents the core loss calculation in soft magnetic composite (SMC) samples and a claw pole permanent magnet machine with SMC stator. By using finite-element analysis of the magnetic field, the total core loss is computed by separating the hysteresis (alternating and rotational, both purely circular and elliptical), eddy current, and anomalous losses in each element when the rotor rotates. The coefficients for each loss component are determined by a loss separation procedure and the experimental data obtained by a single sheet two-dimensional core loss testing system.

A method of fundamental solutions for modeling porous media advective fluid flow

A new numerical scheme for modeling advective tracer flow in oil reservoirs and aquifers is presented. It combines the method of fundamental solutions and a streamline time of flight approach for solving the pressure and concentration equations respectively. Computational results on a variety of two-dimensional problems and validation tests show that the new scheme is free of numerical diffusion, eliminates time step stability restrictions, and is faster than standard boundary element techniques.

A Numerical Method for General Relativistic Magnetohydrodynamics

This paper describes the development and testing of a general relativistic magnetohydrodynamic (GRMHD) code to study ideal MHD in the fixed background of a Kerr black hole. The code is a direct extension of the hydrodynamic code of Hawley, Smarr, and Wilson, and uses Evans and Hawley constrained transport (CT) to evolve the magnetic fields. Two categories of test cases were undertaken. A one dimensional version of the code (Minkowski metric) was used to verify code performance in the special relativistic limit. The tests include Alfv\'en wave propagation, fast and slow magnetosonic shocks, rarefaction waves, and both relativistic and non-relativistic shock tubes. A series of one- and two-dimensional tests were also carried out in the Kerr metric: magnetized Bondi inflow, a magnetized inflow test due to Gammie, and two-dimensional magnetized constant-$l$ tori that are subject to the magnetorotational instability.

A mixed markers and volume-of-fluid method for the reconstruction and advection of interfaces in two-phase and free-boundary flows

In this work we present a new mixed markers and volume-of-fluid (VOF) algorithm for the reconstruction and advection of interfaces in the two-dimensional space. The interface is described by using both the volume fraction function C, as in VOF methods, and surface markers, which locate the interface within the computational cells. The C field and the markers are advected by following the streamlines. New markers are determined by computing the intersections of the advected interface with the grid lines, then other markers are added inside each cut cell to conserve the volume fraction C. A smooth motion of the interface is obtained, typical of the marker approach, with a good volume conservation, as in standard VOF methods. In this article we consider a few typical two-dimensional tests and compare the results of the mixed algorithm with those obtained with VOF methods. Translations, rotations and vortex tests are performed showing that many problems of the VOF technique can be solved and a good accuracy in the geometrical motion and mass conservation can be achieved.

Solving Multi-dimensional Evolution Problems with Localized Structures using Second Generation Wavelets

A dynamically adaptive numerical method for solving multi-dimensional evolution problems with localized structures is developed. The method is based on the general class of multi-dimensional second-generation wavelets and is an extension of the second-generation wavelet collocation method of Vasilyev and Bowman to two and higher dimensions and irregular sampling intervals. Wavelet decomposition is used for grid adaptation and interpolation, while O ( N ) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The prowess and computational efficiency of the method are demonstrated for the solution of a number of two-dimensional test problems.

The Effects of Storage Temperature on the Staling of Wheat Flour Tortillas

Abstract Wheat flour tortillas (31·9% moisture) were stored at −60, −12, 0, 4, 22, and 35 °C to evaluate textural changes during staling. Subjective rollability and two-dimensional extensibility tests revealed that tortillas stored at ≥0 °C had increasing force, work and modulus of deformation values during storage. Tortillas stored at ≤−12 °C retained their fresh attributes over 25 days. Tortillas staled more as defined by rheological changes when stored at 22 °C than at 0, 4, or 35 °C. Optimum storage temperatures of wheat flour tortillas are ≤−12 °C while optimum staling temperatures are between 4 and 35 °C.

Stabilizing Burden Trajectory into Blast Furnace Top under High Ore to Coke Ratio Operation

It becomes still more important to control the falling trajectory in order to stabilize burden distribution control under intensive coal injection in a blast furnace. The present report clarifies the effect of ore falling trajectory on coke collapse in a two-dimensional bell-less burden distribution test and the effect of burden particle size on the falling trajectory, which serves as a disturbance factor. There has been no analysis on the motion on a bell-less rotating chute and falling parabolic motion as a mass flow, and particle dynamics are applied, and it is presently difficult to predict changes of the falling trajectory as a mass flow. Therefore, a falling trajectory measuring technique was developed utilizing acceleration sensors that can continuously measure the falling trajectory of burdens, in particular, the main stream position and the falling width, and was actually applied to Kobe BF3 (3rd campaign) (inner volume: 1845 m3; blown in on April 5, 1983). It has been confirmed that this falling trajectory measuring technique has enabled the measurement of the falling trajectory which is subject to centrifugal force on the rotating chute, a discharge flow rate from a top hopper, and particle size segregation, and which varies in time series, and furthermore, the physical main stream position that is determined by the mass flow rate can be determined uniquely.

On the Efficiency of a Global Non-differentiable Optimization Algorithm Based on the Method of Optimal Set Partitioning

The examined algorithm for global optimization of the multiextremal non-differentiable function is based on the following idea: the problem of determination of the global minimum point of the function f(x) on the set Ω(f(x) has a finite number of local minima in this domain) is reduced to the problem of finding all local minima and their attraction spheres with a consequent choice of the global minimum point among them. This reduction is made by application of the optimal set partitioning method. The proposed algorithm is evaluated on a set of well-known one-dimensional, two-dimensional and three-dimensional test functions. Recommendations for choosing the algorithm parameters are given.

On the frictionless unilateral contact of two viscoelastic bodies

We consider a mathematical model which describes the quasistatic contact between two deformable bodies. The bodies are assumed to have a viscoelastic behavior that we model with Kelvin‐Voigt constitutive law. The contact is frictionless and is modeled with the classical Signorini condition with zero‐gap function. We derive a variational formulation of the problem and prove the existence of a unique weak solution to the model by using arguments of evolution equations with maximal monotone operators. We also prove that the solution converges to the solution of the corresponding elastic problem, as the viscosity tensors converge to zero. We then consider a fully discrete approximation of the problem, based on the augmented Lagrangian approach, and present numerical results of two‐dimensional test problems.

An Adjoint Sensitivity Method for the Adaptive Location of the Observations in Air Quality Modeling

The spatiotemporal distribution of observations plays an essential role in the data assimilation process. An adjoint sensitivity method is applied to the problem of adaptive location of the observational system for a nonlinear transport-chemistry model in the context of 4D variational data assimilation. The method is presented in a general framework and it is shown that in addition to the initial state of the model, sensitivity with respect to emission and deposition rates and certain types of boundary values may be obtained at a minimal additional cost. The adjoint modeling is used to evaluate the influence function and to identify the domain of influence associated with the observations. These essential tools are further used to develop a novel algorithm for targeting observations that takes into account the interaction among observations at different instants in time and spatial locations. Issues related to the case of multiple observations are addressed and it is shown that by using the adjoint modeling an efficient implementation may be achieved. Computational and practical aspects are discussed and this analysis indicates that it is feasible to implement the proposed method for comprehensive air quality models. Numerical experiments performed with a two-dimensional test model show promising results.

Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations

The results of computations with eight explicit finite difference schemes on a suite of one-dimensional and two-dimensional test problems for the Euler equations are presented in various formats. Both dimensionally split and two-dimensional schemes are represented, as are central and upwind-biased methods, and all are at least second-order accurate.

Mesh Moving Techniques for Fluid-Structure Interactions With Large Displacements

In computation of fluid-structure interactions, we use mesh update methods consisting of mesh-moving and remeshing-as-needed. When the geometries are complex and the structural displacements are large, it becomes even more important that the mesh moving techniques are designed with the objective to reduce the frequency of remeshing. To that end, we present here mesh moving techniques where the motion of the nodes is governed by the equations of elasticity, with selective treatment of mesh deformation based on element sizes as well as deformation modes in terms of shape and volume changes. We also present results from application of these techniques to a set of two-dimensional test cases.

FW TO BUILD 600 MW POWER PLANT IN PENNSYLVANIA

Calculations of efficiencies of axial-flow steam turbines have been based for many years upon experimentally determined velocity coefficients. A great amount of uncorrelated data is available. Efficiency calculations for axial-flow gas turbines have been based on loss coefficients obtained from two-dimensional cascade tests, and some correlation of this data has been attempted, notably by Ainley and Mathieson1. The present paper attempts to bring together the two sets of data and the differing nomenclature and approaches of the steam-turbine designer and the gas-turbine designer. Areas are indicated where further research would be useful.