Application of an Implicit Relaxation Method Solving the Euler Equations for Time-Accurate Unsteady Problems

1990 ◽  
Vol 112 (4) ◽  
pp. 510-520 ◽  
Author(s):  
A. Brenneis ◽  
A. Eberle
Keyword(s):  
Euler Equations ◽  
Computing Time ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Relaxation Method ◽  
Coefficient Matrix ◽  
Viscous Effects ◽  
Left Hand ◽  
Implicit Equations ◽  
The Right

A numerical procedure is presented for computing time-accurate solutions of flows about two and three-dimensional configurations using the Euler equations in conservative form. A nonlinear Newton method is applied to solve the unfactored implicit equations. Relaxation is performed with a point Gauss-Seidel algorithm ensuring a high degree of vectorization by employing the so-called checkerboard scheme. The fundamental feature of the Euler solver is a characteristic variable splitting scheme (Godunov-type averaging procedure, linear locally one-dimensional Riemann solver) based on an eigenvalue analysis for the calculation of the fluxes. The true Jacobians of the fluxes on the right-hand side are used on the left-hand side of the first order in time-discretized Euler equations. A simple matrix conditioning needing only few operations is employed to evade singular behavior of the coefficient matrix. Numerical results are presented for transonic flows about harmonically pitching airfoils and wings. Comparisons with experiments show good agreement except in regions where viscous effects are evident.

scholarly journals Multigrain indexing of unknown multiphase materials

2016 ◽  
Vol 49 (2) ◽  
pp. 616-621 ◽  
Author(s):  
Christian Wejdemann ◽  
Henning Friis Poulsen
Keyword(s):  
A Priori ◽  
Computing Time ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Complex Samples ◽  
Multiphase Materials ◽  
Mineral Phases ◽  
Dirac Comb ◽  
Crystallographic Planes ◽  
The Right

A multigrain indexing algorithm for use with samples comprising an arbitrary number of known or unknown phases is presented. No a priori crystallographic knowledge is required. The algorithm applies to data acquired with a monochromatic beam and a conventional two-dimensional detector for diffraction. Initially, candidate grains are found by searching for crystallographic planes, using a Dirac comb convoluted with a box function as a filter. Next, candidate grains are validated and the unit cell is optimized. The algorithm is validated by simulations. Simulations of 500 cementite grains and ∼100 reflections per grain resulted in 99.2% of all grains being indexed correctly and 99.5% of the reflections becoming associated with the right grain. Simulations with 200 grains associated with four mineral phases and 50–700 reflections per grain resulted in 99.9% of all grains being indexed correctly and 99.9% of the reflections becoming associated with the right grain. The main limitation is in terms of overlap of diffraction spots and computing time. Potential areas of use include three-dimensional grain mapping, structural solution and refinement studies of complex samples, and studies of dilute phases.

Prediction of Steady and Unsteady Loads and Hydrodynamic Forces on Counterrotating Propellers

1983 ◽  
Vol 27 (03) ◽  
pp. 197-214
Author(s):  
S. Tsakonas ◽  
W. R. Jacobs ◽  
P. Liao
Keyword(s):  
High Speed ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Viscous Effects ◽  
Sweep Angle ◽  
Helicoidal Surface ◽  
Unequal Number ◽  
Unsteady Loading ◽  
Propeller Blades

Linearized unsteady-lifting-surface theory has been applied in the study of counterrotating propeller systems with equal or unequal number of blades operating in uniform or nonuniform inflow fields when both units are rotating with the same rpm. The mathematical model takes into account as realistically as possible the geometry of the propulsive device, the mutual interaction of both units and the three-dimensional spatially varying inflow field. The propeller blades lie on a helicoidal surface of varying pitch, have finite thickness and arbitrary planform, camber and sweep angle. The inflow field of the after propeller is modified by taking into account the effect of the race of the forward propeller, so that potential and viscous effects of the forward propeller are incorporated. These additional effects play an important role in determining the unsteady loading of the after propeller. This, together with some refinements introduced in the numerical procedure, has brought the theoretical results into better agreement with experiments. A computer program has been developed adaptable to a high-speed digital computer (CDC 6600-7600, Cyber 176) for counterrotating systems of equal and unequal number of blades, in uniform flow, for comparison with existing experiments.

CT Image Measurement and Analysis of the Influence of Different Motion Modes on the Geometrical Morphology of Carpal Bone

2020 ◽  
Vol 10 (4) ◽  
pp. 913-917
Author(s):  
Zegang Wang
Keyword(s):  
Three Dimensional ◽  
Ct Imaging ◽  
Bone Volume ◽  
Carpal Bone ◽  
Left Hand ◽  
Motion Modes ◽  
Measurement And Analysis ◽  
The Difference ◽  
The Right ◽  
Capitate Bone

The purpose of this study is to explore the influence of different movement modes on the geometrical morphology of carpal bones. In this study, Computed Tomography (CT) imaging is used for measurement and analysis. The results show that the changes of wrist bone volume of athletes are not significant compared with that of non-athletes, and the changes of bone density of the wrist bone are more obvious under the motion stress stimulation. According to results of CT imaging measurement and calculation, the average CT values of triangular bone, trapezoid bone, capitate bone and pisiform bone in the left hand and hamate bone in the right hand of the athlete are greater than that of the non-athlete, and the difference is statistically significant. Therefore, CT imaging technology can help to reconstruct the three-dimensional image of the carpal bone and deeply understand the geometric shape of the carpal bone of athletes.

Color constancy by asymmetric color matching with real objects in three-dimensional scenes

2004 ◽  
Vol 21 (3) ◽  
pp. 341-345 ◽  
Author(s):  
VASCO M.N. de ALMEIDA ◽  
PAULO T. FIADEIRO ◽  
SÉRGIO M.C. NASCIMENTO
Keyword(s):  
Color Constancy ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Natural World ◽  
Color Temperature ◽  
Color Matching ◽  
Left Hand ◽  
Real Scene ◽  
Real Objects ◽  
The Right

Color matching experiments use, in general, stimuli that are poor representations of the natural world. The aim of this work was to compare the degree of color constancy for a range of illuminant pairs using a new matching technique that uses both real objects and three-dimensional (3-D) real scenes. In the experiment, observers viewed a 3-D real scene through a large beamsplitter that projects on the right-hand side of the scene (match scene), the virtual image of a 3-D object (match object) such it appeared part of the scene. On the left-hand side of the scene (test scene), observers viewed a symmetrical scene containing a test object identical to the match object. Test and match objects were both surrounded by the same reflectances with identical spatial arrangement. The illuminant on the test scene had always a correlated color temperature of 25,000 K. The illuminant on the match scene could be any of seven different illuminants with correlated color temperatures in the range 25,000 K–4000 K. In each trial, the observers, who were instructed to perform surface color matches, adjusted the illuminant on the match object. Constancy indices were very high (0.81–0.93), varied with the color of the match object, and increased with the extent of the illuminant change. Observer's mismatches, however, were independent of the extent of the illuminant change.

scholarly journals On the Merits of Using a 3D-FGAT Assimilation Scheme with an Outer Loop for Atmospheric Situations Governed by Transport

2010 ◽  
Vol 138 (12) ◽  
pp. 4509-4522 ◽  
Author(s):  
Sébastien Massart ◽  
Benjamin Pajot ◽  
Andrea Piacentini ◽  
Olivier Pannekoucke
Keyword(s):  
Transport Model ◽  
Computing Time ◽  
Three Dimensional ◽  
Observation Time ◽  
Chemical Transport Model ◽  
Outer Loop ◽  
Pros And Cons ◽  
The One ◽  
The Right ◽  
Assimilation Scheme

Abstract Three-dimensional variational data assimilation (3D-Var) with the first guess at appropriate time (FGAT) appears to be an attractive compromise between accuracy and overall computing time. It is computationally cheaper than four-dimensional (4D)-Var as the increment is not propagated back and forth in time by a model, yet the comparison between the model and the observations is still computed at the right observation time. An interesting feature of the 4D-Var is the iterative process known as the outer loop. This outer-loop approach can also be used in conjunction with 3D-FGAT. But it requires the application of the 3D-FGAT analysis increment at the beginning of the assimilation window. The pros and cons of using this unusual 3D-FGAT variant are illustrated in this paper on two applications focused on the transport, one of the main phenomena governing the atmospheric evolution. The first one is the one-dimensional advection of a passive tracer. By three representative situations, it shows the benefits of the outer loop, except for practical situations driven by very rapid dynamics such as a zonal wind of 50 m s−1 on the earth’s great circle, when the assimilation window has a size of 3 h. The second application is the 3D-FGAT assimilation of true ozone measurements into a chemical–transport model. It confirms the previous results, showing that the 3D-FGAT analysis with the outer loop produces an overestimation of the ozone increment in regions where the wind speed is high compared to the time length of the assimilation window.

Three-dimensional printed prosthesis demonstrates functional improvement in a patient with an amputated thumb: A technical note

2016 ◽  
Vol 42 (1) ◽  
pp. 107-111 ◽  
Author(s):  
Keun Ho Lee ◽  
Sung Jae Kim ◽  
Yong Ho Cha ◽  
Jae Lim Kim ◽  
Dong Kyu Kim ◽  
...  
Keyword(s):  
Low Cost ◽  
Hand Function ◽  
Three Dimensional ◽  
Metacarpophalangeal Joint ◽  
Technical Note ◽  
Functional Improvement ◽  
Fused Filament Fabrication ◽  
Left Hand ◽  
Finger Prosthesis ◽  
The Right

Background and Aim: Three-dimensional printer is widely used in industry, biology, and medical fields. We report a finger prosthesis produced by a three-dimensional scanner and printer for a 67-year-old man with a right thumb amputation above the metacarpophalangeal joint. Technique: His right amputated and left intact hands were scanned with a three-dimensional scanner, and the left-hand image was rotated to the right side to design the right thumb prosthesis. The designed prosthesis was printed with a three-dimensional printer using the fused filament fabrication output system. Discussion: The Jebsen–Taylor hand function test and Box and Block Test scores improved after application of the prosthesis. Most Quebec User Evaluation of Satisfaction with Assistive Technology results were “very satisfied,” and most Orthotics and Prosthetics Users’ Survey results were “very easy.” Preparing the prosthesis made by three-dimensional scanner and three-dimensional printer was faster and cheaper than preparing a conventional prosthesis. Clinical relevance Using three-dimensional scanning and printing technique, we can easily produce specifically shaped finger prostheses for specific movements in amputated patients with low cost.

Dynamics of Double Hand Thoracic Spinal Manipulations by Different Chiropractors

2010 ◽  
Author(s):  
Maruti Ram Gudavalli
Keyword(s):  
Three Dimensional ◽  
Shear Forces ◽  
Left Hand ◽  
Peak Loads ◽  
Force Transducers ◽  
Thoracic Spinal ◽  
Load Characteristics ◽  
The Right ◽  
Right And Left Hands ◽  
Right And Left Hand

This study presents the dynamic load characteristics of chiropractors delivering posterior to anterior double thenar thoracic spinal manipulations to a mannequin. A total of 36 thrusts were delivered by the three chiropractors to a mannequin that has similar shape and texture of a human. Two three-dimensional force transducers were used between the doctor’s hand and the mannequin. Parameters of the duration, rate of loading, preload and peak loads were extracted from the data for the three chiropractors. Average peak loads in the normal direction reached 247 N and 217N in the right and left hands. The shear forces reached 36 and 18N in the right and left hand. The rates of loading have reached 804N/s and 761N/s in the right and left hands. Average durations of thrust were 242msecs. The three doctors had distinct characteristics in pre loads, durations of loading and rates of loading.

Three-Dimensional Solutions for Inviscid Incompressible Flow in Turbomachines

1989 ◽  
Author(s):  
S. Abdallah ◽  
C. F. Smith
Keyword(s):  
Experimental Data ◽  
Poisson Equation ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Type Equation ◽  
Neumann Boundary ◽  
Relaxation Method ◽  
Staggered Grid ◽  
Pressure Poisson Equation

A primitive variable formulation is used for the solution of the incompressible Euler’s equation. In particular, the pressure Poisson equation approach using a non-staggered grid is considered. In this approach, the velocity field is calculated from the unsteady momentum equation by marching in time. The continuity equation is replaced by a Poisson-type equation for the pressure with Neumann boundary conditions. A consistent finite-difference method, which insures the satisfaction of a compatibility condition necessary for convergence, is used in the solution of the pressure equation on a non-staggered grid. Numerical solutions of the momentum equations are obtained using the second order upwind differencing scheme, while the pressure Poisson equation is solved using the line successive over-relaxation method. Three turbomachinery rotors are tested to validate the numerical procedure. The three rotor blades have been designed to have similar loading distributions but different amounts of dihedral. Numerical solutions are obtained and compared with experimental data in terms of the velocity components and exit swirl angles. The computed results are in good agreement with the experimental data.

A three-dimensional compressible flow model for rotating waves in vaneless diffusers with unparallel walls

2012 ◽  
Vol 226 (9) ◽  
pp. 2230-2249 ◽  
Author(s):  
Feng Sheng ◽  
Hua Chen ◽  
Xiao-cheng Zhu ◽  
Zhao-hui Du
Keyword(s):  
Compressible Flow ◽  
Euler Equations ◽  
Flow Model ◽  
Three Dimensional ◽  
Rotating Stall ◽  
Experimental Result ◽  
Viscous Effects ◽  
Rotating Waves ◽  
Vaneless Diffusers ◽  
Suppression Effects

A three-dimensional compressible flow model is presented to study the occurrence of weak rotating waves in unparallel wall vaneless diffusers in centrifugal compressors. The model extends the three-dimensional compressible flow model for parallel wall diffusers recently developed by present authors. Linearised three-dimensional compressible Euler equations casted on a rotating frame of reference travelling at the same speeds as the waves are employed and the viscous effects are ignored. Complex functions of the solutions to the linearised Euler equations are then obtained by a second-order finite difference method and the singular value decomposition technique. Undisturbed flow is assumed potential and first solved by numerical method of strongly implicit procedure. Critical inlet flow rate and rotating wave speed of diffusers of three different shroud wall shapes, namely, convergent, convergent then divergent and constant area tapered, are studied for three different diffuser outlet-to-inlet radius ratios and for different inlet Mach numbers, and results compared with those from diffusers with parallel walls. The results show suppression effects on rotating stall by the contracting walls and the suppression effects vary with wall contraction rate, wall shape, inlet Mach number and the diffuser radius ratio. Further, the effects of diffuser inlet contraction are studied and prediction of the model is compared with experimental result.

scholarly journals Viscous Flows in Centrifugal Compressor Diffusers at Transonic Mach Numbers

1992 ◽  
Author(s):  
I. Teipel ◽  
A. Wiedermann ◽  
W. Evers
Keyword(s):  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Flow Fields ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Accelerate Convergence ◽  
Mach Numbers

A numerical investigation of steady two- and three-dimensional flow fields in vaned diffusers of highly-loaded centrifugal compressors is described. The explicit MacCormack scheme was used to calculate inviscid and viscous effects because of the possibility of vectorization. Transonic Mach numbers are reached in the entrance of the diffuser and therefore time-dependent equations are solved. Two methods are employed to accelerate convergence of this explicit scheme. These techniques are (1) local time stepping and (2) applying a multigrid scheme. For the turbulent case an improved Baldwin-Lomax model given by Granville has been used. The numerical procedure has been used to compute two-dimensional transonic flow fields of a centrifugal compressor diffuser at different impeller speeds. It is shown that the predicted pressure field is in reasonable agreement with experimental data. Different approaches for the evaluation of global loss figures have been compared with each other. In addition, an evaluation of the complete three-dimensional Navier-Stokes equations is presented. The vanes in the diffuser are twisted such that the flow field contains a strong three-dimensional effect. Again a comparison with experiments is carried out and the agreement is fairly good.

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