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1
Rüger, Andreas, and Dave Hale. "Meshing for velocity modeling and ray tracing in complex velocity fields." GEOPHYSICS 71, no. 1 (2006): U1—U11. http://dx.doi.org/10.1190/1.2159061.
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In seismic processing, velocity fields are commonly represented on finely sampled Cartesian grids. Attractive alternatives are unstructured grids such as meshes composed of triangles or tetrahedra. Meshes provide a space-filling framework that enables editing of velocity models while facilitating numerical tasks such as seismic modeling and inversion. In this paper, we introduce an automated process to generate meshes of subsurface velocity structures for highly resolved velocity fields without providing additional external constraints such as horizons and faults. Our analysis shows that these new meshes can represent both smooth and discontinuous velocity profiles accurately and with less computer memory than grids.
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Avitzur, B., W. Gordon, and S. Talbert. "Analysis of Strip Rolling by the Upper Bound Approach." Journal of Engineering for Industry 109, no. 4 (1987): 338–46. http://dx.doi.org/10.1115/1.3187137.
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The process of strip rolling is analyzed using the upper bound technique. Two triangular velocity fields, one with triangles in linear rigid body motion and the other with triangles in rotational rigid body motion, are developed. The total power is determined as a function of the four independent process parameters (relative thickness, reduction, friction and net front-back tension). The results of these two velocity fields are compared with the established solution from Avitzur’s velocity field of continuous deformation. Upon establishing the validity of the triangular velocity field as an approach to the strip rolling problem, recommendations are suggested on how this approach can be used to study the split end or alligatoring defect.
3
Gu, Yun Qing, Jing Ru, Zhao Gang, Zhao Yuan Li, Wen Bo Liu, and Muhammad Farid Khattak. "Influence of Jet Hole Configuration on Drag Reduction of Bionic Jet Surface." Applied Mechanics and Materials 461 (November 2013): 725–30. http://dx.doi.org/10.4028/www.scientific.net/amm.461.725.
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According to the jet hole configuration mode of bionic jet surface and its influence on the drag reduction, as the basic form of jet hole configuration is the isosceles triangle elements, so this was used to establish the computational model of jet hole configuration. In this case, the height and base of the triangles were considered as variable. The SST k-ω turbulence model was used to simulate and research the drag reduction characteristics of bionic jet surface in different configuration modes of jet holes at the main flow field velocity value of 20m/s and the jet velocity value of 0.4~2.0m/s. Also the influence of different configurations of height and base on drag reduction characteristics of bionic jet surface was studied, which got the optimum size of jet hole configuration. Results show that in triangle configuration elements, the drag reduction characteristics of bionic jet surface can be influenced by the jet hole of different configurations of height and base; the drag reduction of bionic jet surface reaches the peak of 32.74% at 8mm height, 11mm base, and the jet velocity value of 2.0m/s. At the same flow field velocity, the drag reduction rate results achieved by experimental tests and by numerical simulation were changing consistently and were found same, which verifies correctness of numerical simulation results.
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Averbeck, Bruno B., Matthew V. Chafee, David A. Crowe, and Apostolos P. Georgopoulos. "Parietal Representation of Hand Velocity in a Copy Task." Journal of Neurophysiology 93, no. 1 (2005): 508–18. http://dx.doi.org/10.1152/jn.00357.2004.
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We recorded neural activity from ensembles of neurons in areas 5 and 2 of parietal cortex, while two monkeys copied triangles, squares, trapezoids, and inverted triangles and used both linear and nonlinear models to predict the hand velocity from the neural activity of the ensembles. The linear model generally outperformed the nonlinear model, suggesting a reasonably linear relation between the neural activity and the hand velocity. We also found that the average transfer function of the linear model fit to individual cells was a low-pass filter because the neural response had considerable high-frequency power, whereas the hand velocity only had power at frequencies below ∼5 Hz. Increasing the width of the transfer function, up to a width of 700–800 ms, improved the fit of the model. Furthermore, the Rsqr of the linear model improved monotonically with the number of cells in the ensemble, saturating at 60–80% for a filter width of 700 ms. Finally, it was found that including an interaction term, which allowed the transfer function to shift with the eye position, did not improve the fit of the model. Thus ensemble neural responses in superior parietal cortex provide a high-fidelity, linear representation of hand kinematics within our task.
5
Pennock, Gordon R., and Patrick J. Meehan. "Geometric Insight Into the Dynamics of a Rigid Body Using the Spatial Triangle of Screws." Journal of Mechanical Design 124, no. 4 (2002): 684–89. http://dx.doi.org/10.1115/1.1500340.
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Geometric relationships between the velocity screw and momentum screw are presented, and the dual angle between these two screws is shown to provide important insight into the kinetics of a rigid body. Then the centripetal screw is defined, and the significance of this screw in a study of the dynamics of a rigid body is explained. The dual-Euler equation, which is the dual form of the Newton-Euler equations of motion, is shown to be a spatial triangle. The vertices of the triangle are the centripetal screw, the time rate of change of momentum screw, and the force screw. The sides of the triangles are three dual angles between the three vertices. The spatial triangle provides valuable geometrical insight into the dynamics of a rigid body and is believed to be a meaningful alternative to existing analytical techniques. The authors believe that the work presented in this paper will prove useful in a dynamic analysis of closed-loop spatial mechanisms and multi-rigid body open-chain systems.
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Selzer, Philipp, and Olaf A. Cirpka. "Postprocessing of standard finite element velocity fields for accurate particle tracking applied to groundwater flow." Computational Geosciences 24, no. 4 (2020): 1605–24. http://dx.doi.org/10.1007/s10596-020-09969-y.
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Abstract Particle tracking is a computationally advantageous and fast scheme to determine travel times and trajectories in subsurface hydrology. Accurate particle tracking requires element-wise mass-conservative, conforming velocity fields. This condition is not fulfilled by the standard linear Galerkin finite element method (FEM). We present a projection, which maps a non-conforming, element-wise given velocity field, computed on triangles and tetrahedra, onto a conforming velocity field in lowest-order Raviart-Thomas-Nédélec ($\mathcal {RTN}_{0}$ R T N 0 ) space, which meets the requirements of accurate particle tracking. The projection is based on minimizing the difference in the hydraulic gradients at the element centroids between the standard FEM solution and the hydraulic gradients consistent with the $\mathcal {RTN}_{0}$ R T N 0 velocity field imposing element-wise mass conservation. Using the conforming velocity field in $\mathcal {RTN}_{0}$ R T N 0 space on triangles and tetrahedra, we present semi-analytical particle tracking methods for divergent and non-divergent flow. We compare the results with those obtained by a cell-centered finite volume method defined for the same elements, and a test case considering hydraulic anisotropy to an analytical solution. The velocity fields and associated particle trajectories based on the projection of the standard FEM solution are comparable to those resulting from the finite volume method, but the projected fields are smoother within zones of piecewise uniform hydraulic conductivity. While the $\mathcal {RTN}_{0}$ R T N 0 -projected standard FEM solution is thus more accurate, the computational costs of the cell-centered finite volume approach are considerably smaller.
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Liebold, Frank, Ali A. Heravi, Oliver Mosig, Manfred Curbach, Viktor Mechtcherine, and Hans-Gerd Maas. "Crack Propagation Velocity Determination by High-speed Camera Image Sequence Processing." Materials 13, no. 19 (2020): 4415. http://dx.doi.org/10.3390/ma13194415.
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The determination of crack propagation velocities can provide valuable information for a better understanding of damage processes of concrete. The spatio-temporal analysis of crack patterns developing at a speed of several hundred meters per second is a rather challenging task. In the paper, a photogrammetric procedure for the determination of crack propagation velocities in concrete specimens using high-speed camera image sequences is presented. A cascaded image sequence processing which starts with the computation of displacement vector fields for a dense pattern of points on the specimen’s surface between consecutive time steps of the image sequence chain has been developed. These surface points are triangulated into a mesh, and as representations of cracks, discontinuities in the displacement vector fields are found by a deformation analysis applied to all triangles of the mesh. Connected components of the deformed triangles are computed using region-growing techniques. Then, the crack tips are determined using the principal component analysis. The tips are tracked in the image sequence and the velocities between the time stamps of the images are derived. A major advantage of this method as compared to the established techniques is in the fact that it allows spatio-temporally resolved, full-field measurements rather than point-wise measurements. Furthermore, information on the crack width can be obtained simultaneously. To validate the experimentation, the authors processed image sequences of tests on four compact-tension specimens performed on a split-Hopkinson tension bar. The images were taken by a high-speed camera at a frame rate of 160,000 images per second. By applying the developed image sequence processing procedure to these datasets, crack propagation velocities of about 800 m/s were determined with a precision in the order of 50 m/s.
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Xing, Weiwei, Jian Zhang, Wei Lu, and Peng Bao. "An Improved Potential Field Based Method for Crowd Simulation." International Journal of Software Engineering and Knowledge Engineering 25, no. 03 (2015): 427–51. http://dx.doi.org/10.1142/s021819401540015x.
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Crowd simulation explores crowd behavior in virtual environments, which has been extensively studied in many areas, such as safety and civil engineering, transportation, social science, and entertainment industry. In this paper, an improved potential field method is proposed to achieve the real-time crowd simulation, which is composed of the global navigation with Dijkstra's algorithm and the potential field based local navigation. First, a region separation is performed to divide the environment into a set of triangles, and thus a topological graph can be built with the triangles as vertices. Then a velocity-density model is introduced for improving the speed controlling mechanism and solving the "maximum speed dilemma" which means the velocity of an individual derived by potential field will be stuck into the maximum due to the ill speed control. Since the movement of an individual in the crowd is influenced by the socio-psychological forces, the individuals' actions express the group attributes. In order to represent the group attributes in the crowd, the repulsive potential function is improved in this paper. Experiments have been carried out and the results show that the improved potential field based method can simulate the crowd in real time and avoid the "maximum speed dilemma".
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MULDER, W. A. "HIGHER-ORDER MASS-LUMPED FINITE ELEMENTS FOR THE WAVE EQUATION." Journal of Computational Acoustics 09, no. 02 (2001): 671–80. http://dx.doi.org/10.1142/s0218396x0100067x.
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The finite-element method (FEM) with mass lumping is an efficient scheme for modeling seismic wave propagation in the subsurface, especially in the presence of sharp velocity contrasts and rough topography. A number of numerical simulations for triangles are presented to illustrate the strength of the method. A comparison to the finite-difference method shows that the added complexity of the FEM is amply compensated by its superior accuracy, making the FEM the more efficient approach.
10
Monen, Jos, and Eli Brenner. "Detecting Changes in One's Own Velocity from the Optic Flow." Perception 23, no. 6 (1994): 681–90. http://dx.doi.org/10.1068/p230681.
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Experiments were designed to establish whether we can use the optic flow to detect changes in our own velocity. Subjects were presented with simulations of forward motion across a flat surface. They were asked to respond as quickly as possible to a step increase in simulated ego-velocity. The smallest change for which subjects could respond within 500 ms was determined. At realistic simulated speeds of locomotion, the simulated ego-velocity had to increase by about 50%. The threshold for detecting changes in simulated ego-velocity was hardly better than the threshold for detecting other changes in the acceleration of the dots on the screen. It made little difference whether the surface across which the subject appeared to move was built up of dots, lines, or triangles; neither did it matter whether subjects saw the same image with both eyes, or whether the simulation was presented in stereoscopic depth. The results show that we are very poor at detecting changes in our own velocity on the basis of visual input alone.
11
Yang, Er Long, Yu Xin Gao, and Dong Liang Li. "The Research of the Seepage Regularity of Power-Law Fluid under Porosity Scale." Applied Mechanics and Materials 423-426 (September 2013): 1722–26. http://dx.doi.org/10.4028/www.scientific.net/amm.423-426.1722.
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There are various shapes of capillary tubes in the rock, and the flow in triangles and rectangles capillary tubes has been studied very little. In this paper, the approximate solution of the distribution of the velocity in triangles capillary tubes has been obtained using variational method. The quantitative relation between pressure difference and flow rate in the two kinds of capillary tubes has been obtained by integrating in the entire capillary tubes, which is similar to Poiseuille's law. this study also applies the Pdetool tool in Matlab to solve the laminar flow of different sections in capillary flow numerically and compares the variational results and numerical results with the literature analytic solution, numerical solution and the experimental results. On the foundation of comparing the variational results, the numerical results and the literature analytic solution, numerical solution and the experimental results, we analyze the influence of the power-law index and cross-section shape on the comprehensive resistance coefficient and flow pressure relationship.
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Cader, T., O. Masbernat, and M. C. Roco. "Two-Phase Velocity Distributions and Overall Performance of a Centrifugal Slurry Pump." Journal of Fluids Engineering 116, no. 2 (1994): 316–23. http://dx.doi.org/10.1115/1.2910274.
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Back-scattering LDV has been used to investigate particulate two-phase flow in a centrifugal slurry pump. The measurements reported here have been made with a dilute suspension of 0.8 mm glass beads at the impeller-casing flow interface. This interface is of practical importance because the corresponding velocity and concentration results can be used to determine the pump head and flowrate. The present study evaluates the connection between the liquid and solids velocity distribution measured around the impeller and the pump performance determined from measurements at the pump inlet and outlet. The analysis of the velocity triangles for both phases shows the effect of the pump flowrate and inlet recirculation on the pump head at the impeller outlet, as well as the effect of particle slip on pump energy efficiency. A separate group of characteristic curves is proposed to represent the periodical fluctuations of the pump flowrate, head, and loss of efficiency due to particle slip, as a function of the impeller position.
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Li, Wen-Guang. "Effects of Flow Rate and Viscosity on Slip Factor of Centrifugal Pump Handling Viscous Oils." International Journal of Rotating Machinery 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/317473.
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Slip factor is an important parameter in the hydraulic design of centrifugal pump impeller for handling viscous oils. How to extract the factor from CFD computational results and how flow rate and liquid viscosity to affect it remain unclear. In the present paper, the flip factor was estimated by means of two approaches: one is from the velocity triangles at the impeller outlet and the other is due to the impeller theoretical head of 3D turbulent viscous fluid. The velocity of water and viscous oils in the impeller and volute computed by CFD was validated with LDV measurements at the best efficiency point. The effect of exit blade angle on slip factor was clarified. It was shown that the two approaches result into two different slip factors. The factors are significantly dependent of flow rate; however, the liquid viscosity seems to take less effect on them. Volute is responsible for reduction in tangential velocity of liquid at the outlet of impeller at low flow rates. The slip factor of impeller with large exit blade angle is not sensitive to flow rate.
14
Chang, C. C. "Crossed patch arrangements of linear triangular elements for upper bound finite-element analysis of plane strain deformation problems." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 2 (2010): 280–91. http://dx.doi.org/10.1243/09544062jmes2072.
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In standard linear finite-element formulations, volumetric locking because of the incompressibility constraint that may occur in computational plasticity is often encountered. This study uses crossed patch arrangements of triangles to form quadrilateral elements in order to overcome the locking in the upper bound finite-element analysis of plane strain deformation problems. The velocity field is described in terms of linear triangular elements, while the incompressibility constraint is imposed by quadrilateral elements. Rigid, perfectly plastic materials, and strain hardening materials that form the von Mises model have been considered. The velocity formulation is presented and has been implemented in a finite-element code. Several examples, some benchmarks problems, are presented to illustrate the applicability of the approach for predicting the load, strain, and velocity field during the plastic deformation. Numerical results show that the crossed patch arrangements of linear triangular elements are free of volumetric locking and achieve well-defined limit loads. This study shows that the presented method can be used to simulate large plastic deformation under plane strain conditions.
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Yang, Yuande, Bo Sun, Zemin Wang, et al. "GPS-derived velocity and strain fields around Dome Argus, Antarctica." Journal of Glaciology 60, no. 222 (2014): 735–42. http://dx.doi.org/10.3189/2014jog14j078.
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AbstractKnowledge of the surface topography, velocity field and strain field at an ice-core site is critical to the accurate interpretation of ice-core records. At Dome Argus (Dome A), where a Chinese deep ice-core drilling project is being carried out, we have produced an accurate surface digital elevation model from GPS measurements in January 2013 at 47 sites. We identify two peaks at Dome A, with the northern peak ~7 cm higher than the southern peak. Repeat GPS measurements at 12 sites in 2008 and 2013 provide a surface velocity field around the dome. The surface velocity ranges from 3.1±2.6 to 29.4±1.2 cm a–1, with a mean of 11.1 ~2.4 cm a–1. The surface flow directions are near perpendicular to the surface elevation contours. Velocities from GPS are lower than derived from satellite radar interferometry (InSAR). From GPS velocities, the accuracy of velocity from the existing InSAR velocity field is determined, resulting in a standard deviation of 0.570 m a–1 in speed and 117.5º in direction. This result is consistent with the reported accuracy of InSAR, showing the value of in situ GPS measurements for assessing and correcting remote-sensing results. A surface strain field for the drilling site over Dome A is calculated from 24 strain triangles, showing north–south extension, east– west compression and vertical layer thinning.
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Joachim, Kurzke. "Turbine Map Extension - Theoretical Considerations and Practical Advice." Journal of the Global Power and Propulsion Society 4 (November 26, 2020): 176–89. http://dx.doi.org/10.33737/jgpps/128465.
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Physically sound compressor and turbine maps are the key to accurate aircraft engine performance simulations. Usually, maps only cover the speed range between idle and full power. Simulation of starting, windmilling and re-light requires maps with sub-idle speeds as well as pressure ratios less than unity. Engineers outside industry, universities and research facilities may not have access to the measured rig data or the geometrical data needed for CFD calculations. Whilst research has been made into low speed behavior of turbines, little has been published and no advice is available on how to extrapolate maps. Incompressible theory helps with the extrapolation down to zero flow as in this region the Mach numbers are low. The zero-mass flow limit plays a special role; its shape follows from turbine velocity triangle analysis. Another helpful correlation is how mass flow at a pressure ratio of unity changes with speed. The consideration of velocity triangles together with the enthalpy-entropy diagram leads to the conclusion that in these circumstances flow increases linearly with speed. In the incompressible flow region, a linear relationship exists between torque/flow and flow. The slope is independent of speed and can be found from the speed lines for which data are available. This knowledge helps in extending turbine maps into the regions where pressure ratio is less than unity. The application of the map extension method is demonstrated with an example of a three-stage low pressure turbine designed for a business jet engine.
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SCHÖTZAU, DOMINIK, and CHRISTOPH SCHWAB. "MIXED hp-FEM ON ANISOTROPIC MESHES." Mathematical Models and Methods in Applied Sciences 08, no. 05 (1998): 787–820. http://dx.doi.org/10.1142/s0218202598000366.
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Mixed hp-FEM for incompressible fluid flow on anisotropic meshes are analyzed. A discrete inf–sup condition is proved with a constant independent of the meshwidth and the aspect ratio. For each polynomial degree k≥2 we present velocity-pressure subspace pairs which are stable on quadrilateral mesh-patches independently of the element aspect ratio, implying in particular divergence stability on the so-called Shishkin-meshes. Moreover, the inf–sup constant is shown to depend on the spectral order k like k-1/2 for quadrilateral meshes and like k-3 for meshes containing triangles. New consistency results for spectral elements on anisotropic meshes are also proved.
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Hesketh, J. A., and P. J. Walker. "Effects of Wetness in Steam Turbines." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 219, no. 12 (2005): 1301–14. http://dx.doi.org/10.1243/095440605x32110.
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Courses in mechanical engineering usually introduce the theory of axial-flow turbo-machines in terms of simple velocity triangles representing the bulk flow of ideal compressible fluid through the blade passages. A distinctive practical difference, peculiar to steam turbines (ST), is the presence of liquid-water in the flow field. The steam wetness in such turbines is widely known to be doubly-damaging, leading to both loss of efficiency and to mechanical damage (erosion, etc.) of the machine components. Over recent decades, a whole new field of mechanical engineering science has evolved on the subject of wetness in steam turbines, and general practices have been established within the industry. This article reviews the general effects that are of major importance to the turbine designer/engineer, power plant operator, and especially to researchers in this field.
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Du, Wenhai, and Olivier Léonard. "Numerical Simulation of Surge in Axial Compressor." International Journal of Rotating Machinery 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/164831.
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The object of this paper is to provide a reliable tool to simulate the stationary and transient operation performances in multistage axial compression systems, especially poststall behavior. An adapted version of the 1D Euler equations with additional source terms is solved by a time marching and control volume method. The equations are discretized at midspan both inside the blade rows and the nonbladed regions, along the real flow path geometry. The source terms express the blade-flow interactions and are estimated by calculating the velocity triangles for each blade row. Loss coefficient and deviation models are supplied by empirical correlations and are compared to experimental data in all flow regions. Transient simulations are carried and compared to the experimental results for several values of parameterB. The flow mechanism inside the compressor during a surge cycle is also shown.
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Tisserant, D., and F. A. E. Breugelmans. "Rotor Blade-to-Blade Measurements Using Particle Image Velocimetry." Journal of Turbomachinery 119, no. 2 (1997): 176–81. http://dx.doi.org/10.1115/1.2841096.
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The study of turbomachinery flow fields requires detailed experimental data. The rotating parts of turbomachines greatly limit the measurement techniques that can be used. Particle Image Velocimetry (PIV) appears to be a suitable tool to investigate the blade-to-blade flow in a rotor. The facility is a subsonic axial-flow compressor. The experimental apparatus enables the recording of a double-exposed photograph in a circumferential plane located at 85 percent of the blade height. The illumination plane has an axial direction and is provided by a pulsed ruby laser. The tracers used are submicron glycerine oil droplets. Data are processed by Young’s fringes method. Measurements were performed at 3000, 4500, and 6000 rpm with velocities in the range of 30 to 70 m/s. Steady operating conditions are chosen in such a way that the effect of radial velocity on PIV measurements can be neglected. Experimental problems encountered included homogeneous seeding of the flow field and laser light scattering from blade surfaces. The uncertainty affecting the velocity determination corresponds to 2 percent of the measured value. For a given set of operating conditions, 10 PIV pictures are recorded. The periodic flow field is approximated by averaging the experimental data point by point. Upstream and downstream velocity triangles are confirmed by measurements obtained from pressure probes. PIV measurement results were found to be similar to those of a blade-to-blade potential-flow calculation.
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Zhang, Z. H., Z. J. Yang, and J. H. Li. "An Adaptive Polygonal Scaled Boundary Finite Element Method for Elastodynamics." International Journal of Computational Methods 13, no. 02 (2016): 1640015. http://dx.doi.org/10.1142/s0219876216400156.
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An adaptive polygonal scaled boundary finite element method (APSBFEM) is developed for elastodynamics. Flexible polygonal meshes are generated from background Delaunay triangular meshes and used to calculate structure’s dynamic responses. In each time step, a posteriori-type energy error estimator is employed to locate the polygonal subdomains with exceeding spatial discretization error, then edge midpoints of the corresponding triangles are inserted into the background. A new Delaunay triangular mesh and a polygonal mesh are regenerated successively. The state variables, including displacement, velocity and acceleration are mapped from the old polygonal mesh to the new one by a simple algorithm. A benchmark elastodynamic problem is modeled to validate the developed method. The results show that the adaptive meshes are capable of capturing the steep stress regions, and the dynamic responses agree well with those from the adaptive finite element method and the polygonal scaled boundary finite element method without adaptivity using fine meshes.
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Wu, Cheng-Feng, and Huey-Chu Huang. "Detection of a fracture zone using microtremor array measurement." GEOPHYSICS 84, no. 1 (2019): B33—B40. http://dx.doi.org/10.1190/geo2017-0393.1.
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We have conducted microtremor array measurements to estimate shallow S-wave velocity ([Formula: see text]) structures at two sites (the 921 Earthquake Museum of Taiwan and the Taiwan Provincial Consultative Council) located near surface ruptures of the Chelungpu Fault. Ten stations, consisting of three different-aperture triangles and a central station, are adopted for each array deployment. Using the array data, we calculate dispersion curves of Rayleigh waves using the frequency-wavenumber spectrum method and then estimate [Formula: see text] structures by the surface-wave inversion technique. The obtained 2D [Formula: see text] profiles could clearly show compressive and flexural deformation structures with the surface ruptures located at relatively weak (low [Formula: see text]) zones. This indicates compressive buckling as the most likely mechanism for surface rupturing along these low [Formula: see text] zones. Importantly, this study successfully depicts strata disturbances in a fault fracture zone using microtremor array measurements and forward numerical modeling of trishear fault-propagation folds.
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Worley, Shelby C. "The geometry of reflection." GEOPHYSICS 58, no. 2 (1993): 293–97. http://dx.doi.org/10.1190/1.1443413.
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The two‐dimensional (2-D) reflection path from a dipping plane between an offset source‐receiver combination in a constant velocity medium can be described with several parameters (coordinates, offsets, angles, and lengths). Although there are many parameters, only four independent ones are needed to locally determine the reflection geometry. Given four determining parameters, the evaluations of other ones present problems that range from trivial to formidable. The circumscribed circle about the source, receiver, and specular point turns out to have a number of remarkable properties that are useful for the solution of these problems. The radius of the circle is a useful new auxiliary parameter. Triangles constructed in the circle provide nonintuitive mathematical relationships between angles and lengths. The use of mathematical relations derived from the circle has allowed the creation of formulas to fully recover the reflection geometry in a vast majority of valid sets of four known parameters. This circle provides a powerful tool for the calculation of nondetermining parameters as well as new insight into the geometry of reflection with straight raypaths.
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KANG, HYUNG SUK, DUANE DENNIS, and CHARLES MENEVEAU. "FLOW OVER FRACTALS: DRAG FORCES AND NEAR WAKES." Fractals 19, no. 04 (2011): 387–99. http://dx.doi.org/10.1142/s0218348x1100549x.
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An experimental study of interactions between a high Reynolds number fluid flow and multi-scale, fractal, objects is performed. Studying such interactions is required to improve our current understanding of wind or ocean current effects on vegetation elements, which often display fractal-like branching geometries. The main objectives of the study are to investigate the effects of the range of scales (generation numbers) of the fractal object and of the incoming flow condition on the drag force and drag coefficient, and to observe flow features in the near wake region resulting from the interaction. In this study, Sierpinski carpets and triangles with the scale ratios of 1/3 and 1/2, respectively, are employed. The fractal dimensions of the Sierpinski carpet and triangle are D = 1.893 and 1.585, respectively. Each pre-fractal object is mounted on a load cell at the centerline in a wind tunnel. Two types of inflow conditions are considered: laminar flow and high-turbulence level, active-grid-generated, flow. As a first approximation, we find the drag coefficients are approximately constant of order unity, and do not depend upon generation number of the pre-fractal when defined using the actual frontal area that varies as function of generation number. Still, the drag coefficient of the Sierpinski carpet increases weakly with number of generations indicating that the drag force decreases less than the cross-sectional area. For the Sierpinski triangle a similar trend is observed at large scales. However, the drag coefficient displays a peak at the third generation and then shows a decreasing trend as smaller scales are included for higher generation cases. The drag coefficient for the turbulent flow is larger than that for the laminar flow for all the fractal generations observed. Flow features (mean velocity, mean vorticity, and turbulence root-mean-square distributions) are measured by using stereoscopic Particle Image Velocimetry to observe various scales of the motion in the near wake of the pre-fractal objects. Strong shear layers are formed behind the fractal objects depending on the hole locations of different generations, which results in the formation of various length scales of the dominant turbulence structures. The smaller scale wakes are found to merge behind the Sierpinski carpet, whereas they are merely damped behind the Sierpinski triangle.
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Vinje, Vetle, Ketil Åstebøl, Einar Iversen, and Håvar Gjøystdal. "3-D ray modeling by wavefront construction in open models." GEOPHYSICS 64, no. 6 (1999): 1912–19. http://dx.doi.org/10.1190/1.1444697.
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A synthesis of two newly developed concepts in 3-D modeling is developed in this paper: (1) The open, (noncomplete) seismic model, and (2) the ray tracing based wavefront (WF) construction method. The open model may contain interfaces with holes and other missing parts, which simplifies model building considerably because the input horizon data from standard interpretation and processing packages are often incomplete. A set of volumes is defined in the model. A volume is a logical unit that points to a set of property functions, e.g., P-velocity, S-velocity, and density. The properties are represented either as constants or as B-spline functions of the spatial coordinates (x, y) or (x, y, z). The volumes of the model are assigned to opposing sides of each interface and not to specific spatial areas of the model, which is the case in most (blocky) model representations. The interfaces are given explicitly by triangular grids where the sizes of the triangles are determined locally by the curvature of the interface. We show how modeling by WF construction is both possible and computationally efficient in open models, but only after some modifications to deal with the ambiguity of the model representation. It is not possible to find a unique volume for the spatial positions in an open model. Instead, the volumes (with associated velocities, etc.) are determined from the last interface encountered by each ray in the WF. To find an arrival in a receiver, the volume associated to the receiver has to match the volume of the WF hitting the receiver.
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Arghir, Mihai, and Jean Fre^ne. "A Triangle Based Finite Volume Method for the Integration of Lubrication’s Incompressible Bulk Flow Equations." Journal of Tribology 123, no. 1 (2000): 118–24. http://dx.doi.org/10.1115/1.1326444.
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It is well known that for a reduced Reynolds number Re*=ρVH/μs˙H/L greater than unity, inertia forces have a dominant effect in the transport equations, thus rendering the classical lubrication equation inapplicable. The so called “bulk flow” system of equations is then the appropriate mathematical model for describing the flow in bearing and seals operating at Re*⩾1. The difficulty in integrating this system of equations is that one has to deal with coupled pressure and velocity fields. Analytic methods have a very narrow application range so a numerical method has been proposed by Launder and Leschziner in 1978. It represents a natural extrapolation of the successful SIMPLE algorithm applied to the bulk flow system of equations. The algorithm used rectangular, staggered control volumes and represented the state of the art at that moment. In the present work we introduced a method using triangular control volumes. The basic advantage of triangles versus rectangles is that non rectangular domains can be dealt without any a priori limitation. The present paper is focused on the description of the discretized equations and of the solution algorithm. Validations for bearings and seals operating in incompressible, laminar and turbulent flow regime are finally proving the accuracy of the method.
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Zaher, M. A. "Approximate method for calculating the characteristics of a radial flow pump." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 215, no. 4 (2001): 295–316. http://dx.doi.org/10.1177/095440890121500404.
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Similarity in flow patterns between fans and pumps provides the possibility of suggesting an approximate method for calculating radial flow pump characteristics. The proposed method uses relations expressing the energy balance of real fluids. Calculations of velocity triangles are given for a flow ahead of an impeller operating in sections with half-output, recognized as an average value. The results followed the expression within blade theory for radial impellers. While the exit angle helps to understand the blade shape at the no-lift position, the impeller losses, on the other hand, are related in a certain way to the angle of incidence. Losses at different elements of the pump are treated, at a selected point of operation, as having a constant coefficient of loss. Values of losses are calculated from the actual pressure heads. The flow through spiral bodies takes an approximate kinetic model. A spiral section having the shape of a circle provides the suitable conditions guaranteeing the operation of a single impeller along its circumference while still having the same optimum value of pump efficiency. The illustrated figures are the result of calculations made on radial impellers measured from several pump investigations.
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Moukalled, F., and A. Honein. "Computer-Aided Analysis of the Pelton Wheel." International Journal of Mechanical Engineering Education 23, no. 4 (1995): 297–314. http://dx.doi.org/10.1177/030641909502300403.
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This paper describes PELTON, a microcomputer-based, interactive, and menu-driven software package for use as an educational tool by mechanical and civil engineering students in studying the operation of the Pelton wheel. The program is written in the Pascal computer language and runs on IBM PC, or compatible, computers. The package can handle problems related to impulse turbines by solving for unknown variables through a complete set of equations covering the turbine installation. Model-prototype problems can be tackled through similarity laws. This facility is included to help analysing and manipulating experimental data. Furthermore, the graphical utilities of PELTON allow the user to display diagrammatic sketches of the turbine, to employ some recommended charts, and to draw velocity triangles at several locations. The most important feature of the program, however, is its ability to plot the variation of any variable versus any other one. Through this option, the package guides the student in understanding the effects of varying design parameters on the overall performance of the machine. Finally, a comprehensive example problem is provided to show how user-friendly and encouraging-to-use PELTON is, and to demonstrate the capabilities of the package as an instructional tool.
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Moukalled, F., and A. Honein. "Computer-Aided Analysis of Hydraulic Reaction Turbines." International Journal of Mechanical Engineering Education 25, no. 2 (1997): 73–91. http://dx.doi.org/10.1177/030641909702500201.
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A microcomputer-based educational software package designed to help mechanical engineering students to understand hydraulic reaction turbines is described. The software is interactive, menu-driven, and easy-to-use, is written in the Pascal computer language, and runs on IBM PC, or compatible, computers. The program can handle radial, mixed, or axial flow turbine problems by solving for unknown variables through a complete set of equations covering the turbine installation. Using similarity laws, model-prototype problems or operation under different conditions can also be tackled. Furthermore, the program is equipped with graphical utilities that include many diagrammatic sketches of reaction turbines, some recommended charts, and the possibility of drawing velocity triangles when corresponding variables are available. The most important feature of the package is an option that allows one to plot the variation of any parameter versus any other one. Through this option, the student can easily understand and discuss the effects of varying design parameters on the overall performance of the machine. Finally, some special features that are important in making the package user-friendly and encouraging-to-use are also available, and the comprehensive example problem provided demonstrates the capabilities of the package as an instructional tool.
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Claret, A. "Rotationally and tidally distorted compact stars." Astronomy & Astrophysics 648 (April 2021): A111. http://dx.doi.org/10.1051/0004-6361/202140489.
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Context. To the best of our knowledge, there are no specific calculations of gravity-darkening exponents for white dwarfs in the literature. On the other hand, the number of known eclipsing binaries whose components are tidally and/or rotationally distorted white dwarfs is increasing year on year. Aims. Our main objective is to present the first theoretical approaches to the problem of the distribution of temperatures on the surfaces of compact stars distorted by rotation and/or tides in order to compare with relevant observational data. Methods. We used two methods to calculate the gravity-darkening exponents: (a) a variant of our numerical method based on the triangles strategy and (b) an analytical approach consisting in a generalisation of the von Zeipel theorem for hot white dwarfs. Results. We find discrepancies between the gravity-darkening exponents calculated with our methods and the predictions of the von Zeipel theorem, particularly in the cases of cold white dwarfs; although the discrepancy also applies to higher effective temperatures under determined physical conditions. We find physical connections between the gravity-darkening exponents calculated using our modified method of triangles strategy with the convective efficiency (defined here as the ratio of the convective to the total flux). A connection between the entropy and the gravity-darkening coefficients is also found: variations of the former cause changes in the way the temperature is distributed on distorted stellar surfaces. On the other hand, we have generalised the von Zeipel theorem for the case of hot white dwarfs. Such a generalisation allows us to predict that, under certain circumstances, the value of the gravity-darkening exponent may be smaller than 1.0, even in the case of high effective temperatures. Conclusions. To constrain the gravity-darkening exponent values observationally it would be necessary to find and investigate eclipsing binaries constituted by white dwarfs showing tidal and/or rotational distortions that were double-lined and that were bright enough to obtain good radial-velocity semi-amplitudes for both components. It would be very interesting and useful if observer were to focus their attention on this kind of system to check our theoretical results.
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Кислицын, Степан Александрович, Константин Александрович Митин, and Владимир Степанович Бердников. "Numerical simulation of heat transfer processes during single crystal growth by the Bridgman - Stockbarger method in fixed and rotating crucibles." Вычислительные технологии, no. 1(26) (April 2, 2021): 21–32. http://dx.doi.org/10.25743/ict.2021.26.1.002.
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Численно методом конечных элементов исследованы процессы кристаллизации кремния в плоскодонных неподвижных и равномерно вращающихся графитовых цилиндрических тиглях в режимах сопряженного конвективного теплообмена. Процессы кристаллизации кремния изучены при фиксированной скорости опускания тигля в холодную зону и различных скоростях его вращения. Опускание тигля имитировалось перемещением точки излома в распределении температуры на внешней стороне стенок тигля. Точка излома - это граница перехода от нагретого до начальной температуры участка стенки к области с заданным градиентом температуры. Использованы адаптивные сетки на треугольниках, отслеживающие положение фронта кристаллизации на каждом временном шаге. Использован пакет программ собственной разработки. The dependence of both spatial shape and intensity of the convective flow of silicon melt during the growth of a silicon ingot by the Bridgman-Stockbarger method was studied numerically by the finite element method. Stationary and uniformly rotating graphite crucible in conjugate convective heat transfer regines were examined. The simulation was carried out on the basis of dimensionless system of equations for the thermogravitational convection in the Boussinesq approximation using the bipolar approach. In the mixed convection regine, the system of equations was augmented by an equation for the azimuthal velocity. Adaptive grids on triangles were used to track the position of the crystal-melt interface at each time step. The calculations were carried out at a constant rate of lowering the crucible from the hot to the cold zone, equal to 2.81 cm/h, and at a constant temperature gradient equal to 35 K/cm. Lowering the crucible was simulated by moving the inflection point in the temperature distribution on the outside of the crucible walls. The range of angular velocities of crucible rotation from 0 to 10 rpm is considered. It is shown that as the angular velocity of crucible rotation in the axial region increases, both the velocity of the downward flow arising in the regines of thermogravitational convection gradually and the convective heat flux to the crystal-melt interface decrease. As a result, in the range of angular velocities from 2 to 10 rpm, the shape of the crystal-melt interface gradually approaches to the one typical for the thermal conductivity regime. It is shown that at the initial stage of the process at an angular velocity of 10 rpm in the axial region of the cooled crucible bottom, the nucleation of a single crystal is possible.
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Benhegouga, Islem, and Ce Yang. "Steady Air Injection Flow Control in Centrifugal Compressor." Applied Mechanics and Materials 138-139 (November 2011): 471–77. http://dx.doi.org/10.4028/www.scientific.net/amm.138-139.471.
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In the present work steady air injection upstream of the leading edge was used in a centrifugal compressor, Whose preliminary design of compressor injection systems can be modeled by a geometrical relationship between user-specified yaw angle and resulting blade incidence angle based on simple velocity triangles, the error between the best yaw angle obtained from this relationship and that obtained from numerical simulation is less than 3%. To reveal the mechanism, steady numerical simulations were performed on high pressure ratio centrifugal compressor rotor operated with a rotor tip speed of 586 m/s. Parametric studies of the injection yaw angle was performed to determine the configuration that provide the best steady results for the compression systems studied in this work. The injectors were placed at short distance (ten percent of the inlet tip radius upstream of the compressor face) the objective of this was to achieve maximum control over the leading edge flow by varying individual injection parameters. The injection angle, α, was fifteen while the yaw angle, β, was parametrically varied. The results show that at design speed (n= 50 000 r/min) with injection flow rate equal to 3% of the main flow rate and 25 degree air injection yaw angle can lower the mass flow rate at stall for approximately 7.5%.
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Jordal, Kristin, Olav Bollard, and Ake Klang. "Aspects of Cooled Gas Turbine Modeling for the Semi-Closed O2/CO2 Cycle With CO2 Capture." Journal of Engineering for Gas Turbines and Power 126, no. 3 (2004): 507–15. http://dx.doi.org/10.1115/1.1762908.
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In order to capture the behavior of the oxyfuel cycle operating with high combustor-outlet temperature, the impact of blade and vane cooling on cycle performance must be included in the thermodynamic model. As a basis for a future transient model, three thermodynamic models for the cooled gas turbine are described and compared. The first model, known previously from the literature, models expansion as a continuous process with simultaneous heat and work extraction. The second model is a simple stage-by-stage model and the third is a more detailed stage-by-stage model that includes velocity triangles and enables the use of advanced loss correlations. An airbreathing aeroderivative gas turbine is modeled, and the same gas turbine operating in an oxyfuel cycle is studied. The two simple models show very similar performance trends in terms of variation of pressure ratio and turbine inlet temperature in both cases. With the more detailed model, it was found that, without any change of geometry, the turbine rotational speed increases significantly and performance drops for the maintained geometry and pressure ratio. A tentative increase of blade angles or compressor pressure ratio is found to increase turbine performance and decrease rotational speed. This indicates that a turbine will require redesign for operation in the oxyfuel cycle.
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Xu, Chao, Bangrang Di, and Jianxin Wei. "A physical modeling study of seismic features of karst cave reservoirs in the Tarim Basin, China." GEOPHYSICS 81, no. 1 (2016): B31—B41. http://dx.doi.org/10.1190/geo2014-0548.1.
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On seismic migration sections, anomalous bright spots, called the string of beads response (SBR), are common features of carbonate karst reservoirs at the seismic scale in the Tarim Basin, China. To understand the SBR features of different karst caves, which is an important issue for local exploration, we conducted a physical modeling experiment. Within the physical model, we included various single caves with different scales, velocities, shapes, and fluids, as well as multiple caves in different spatial distributions. SBRs of all caves were extracted and summarized from the migration sections. First, we investigated effects of the cave scale, velocity, spatial distribution, shape, and fluids on SBRs. The relative amplitude of SBRs increased with the cave width ranging from 25 to 400 m and decreased with the cave velocity. The SBR split into two new SBRs when the cave height was larger than 100 m. Spatially distributed multiple caves resulted in some special SBRs, such as long SBRs, inclined SBRs, waved SBRs, and chaotic SBRs. The cave shape contribution to SBRs could be neglected in deep strata practically. The relative amplitude of SBRs of caves filled with gas and oil was stronger than those filled with water. Then, we established an interpretation chart of the corresponding relationship between six types of SBRs and their potential caves. Short SBRs were the responses of caves with a height of less than 60 m. Long SBRs corresponded to two kinds of cave units: (1) a single cave with a height between 70 and 100 m and (2) two caves (height less than 60 m) vertically distributed with a small distance (less than 60 m). Chop-shaped SBRs indicated caves with a width of more than 100 m. Inclined SBRs, waved SBRs, and chaotic SBRs corresponded to multiple caves spatially distributed in triangles, rhombuses, and clusters, respectively.
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Minniti, Caterina P., Vandana Sachdev, Hannoush Hwaida, et al. "Higher Myocardial and Skeletal Muscle Microvascular Flow in Sickle Cell Disease Patients on Hydroxyurea." Blood 128, no. 22 (2016): 1020. http://dx.doi.org/10.1182/blood.v128.22.1020.1020.
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Abstract Individuals with SCD have recurrent episodes of ischemia-reperfusion in vital organs, and abnormal microcirculation is considered a major determinant of end organ damage. Hydroxyurea (HU) treatment has been shown to produce ATP- and nitric oxide-mediated vasodilation, and to improve red cells deformability Few tools are available to quantitatively measure microvascular blood flow in vivo. The purpose of this study was to assess the ability of a novel ECHO based imaging modality to assess the effect of hydroxyurea on cardiac and skeletal muscle perfusion in patients with sickle cell anemia. Methods and Results: Twenty-one HBSS/B0 patients, of whom 15 were treated with HU(average daily dose of 18 ± 8 mg/kg/day), underwent brachial artery ultrasound, echocardiography and contrast enhanced ultrasound (CEU) perfusion imaging of deep flexor muscles of the forearm as well as the myocardium at rest and during vasodilator stress with regadenoson ( ClinicalTrials.gov NCT016028090). Quantitative image analysis was performed to obtain microvascular blood volume and flow velocity measurements. Patients on HU had a lower white blood cell count (6.7±2.1 K/uL vs 10.0±2.1 K/uL, p<0.05), higher mean corpuscular volume (103.6±11.5 fL vs 82.5±8.6 fL, p<0.05) , and lower reticulocyte count (9.3±3.4% vs 15.7±5.6%, p<0.05) as well as a trend towards higher hemoglobin (9.4±1.4g/dL vs 7.9±1.1g/dL , p=NS). Table 1. Cardiac output and total myocardial work was not affected by HU treatment and macrovascular flow in the brachial artery was not affected (Figure 1A). In contrast, both skeletal muscle microvascular flow and myocardial microvascular flow was significantly higher in the SCD patients on HU therapy (Figure 1B, 1C). Conclusions: The beneficial effects of HU therapy in SCD are varied, and clinical effects are often seen prior to a rise in fetal hemoglobin. Other effects, such as lower hemolysis, improved red cell deformability, and inhibition of adhesive properties in the microvasculature have been reported. Some of the beneficial effects of HU may be due to stimulation of nitric oxide synthase, induction of cyclic GMP dependent signaling and improved NO bioavailability. Our study indicates that SCD patients on chronic HU therapy have higher levels of myocardial and skeletal muscle microvascular blood flow. Long term studies are necessary to evaluate whether HU reduces end organ damage in SCA. Skeletal muscle and myocardial microvascular blood flow. Each panel shows blood flow in all SCD patients (red filled diamonds), SCD patients not on HU (red open triangles) and SCD patients on HU (red open inverted triangles). Panel A. Skeletal muscle perfusion normalized to hemoglobin (A x β x hemoglobin) Panel B. Myocardial perfusion normalized to hemoglobin level and total myocardial work. Figure 1. Figure 1. Disclosures No relevant conflicts of interest to declare.
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Martinez-Sanchez, M., B. Jaroux, S. J. Song, and S. Yoo. "Measurement of Turbine Blade-Tip Rotordynamic Excitation Forces." Journal of Turbomachinery 117, no. 3 (1995): 384–92. http://dx.doi.org/10.1115/1.2835673.
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This paper presents results of a program to investigate the magnitude, origin, and parametric variations of destabilizing forces that arise in high power turbines due to blade-tip leakage effects. Five different unshrouded turbine configurations and one configuration shrouded with a labyrinth seal were tested with static offsets of the turbine shaft. The forces along and perpendicular to the offset were measured directly with a dynamometer, and were also inferred from velocity triangles and pressure distributions obtained from detailed flow surveys. These two routes yielded values in fair agreement in all cases. For unshrouded turbines, the cross-forces are seen to originate mainly (˜ 2/3) from the classical Alford mechanism (nonuniform work extraction due to varying blade efficiency with tip gap) and about 1/3 from a slightly skewed hub pressure pattern. The direct forces arise mainly (3/4) from this pressure pattern, with the rest due to a slight skewness of the Alford mechanism. The pressure nonuniformity (lower pressures near the widest gap) is seen to arise from a large-scale redistribution of the flow as it approaches the eccentric turbine. The cross-forces are found to increase substantially when the gap is reduced from 3.0 to 1.9 percent of blade height, probably due to viscous blade-tip effects. The forces also increase when the hub gap between stator and rotor decreases. The force coefficient decreases with operating flow coefficient. In the case of the shrouded turbine, most of the forces arise from nonuniform seal pressures. This includes about 80 percent of the transverse forces. The rest appears to come from uneven work extraction (Alford mechanism). Their level is about 50 percent higher than in the unshrouded cases.
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NARDI, ANTONIO. "LA QUADRATURA DELLA VELOCITÀ." Nuncius 3, no. 2 (1988): 27–64. http://dx.doi.org/10.1163/182539178x00312.
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Abstract<title> SUMMARY </title>Galileo's theory of falling bodies assumes that the speed increases as the time. The geometrical representation of such a proportional increment is a sequence of similar triangles. The areas of these triangles are connected with the values of distances traversed. Now, Galileo did he seize and accept that an area could ever represent a distance traversed? The author of this paper tries to show why it is reasonable to conclude, that he did, even if with some comprehensible intellectual trouble related to infinitesimal considerations. In this respect it is important to consider Mersenne's interpretation of galilean Dialogo and Discorsi.
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Corriveau, D., and S. A. Sjolander. "Influence of Loading Distribution on the Off-Design Performance of High-Pressure Turbine Blades." Journal of Turbomachinery 129, no. 3 (2006): 563–71. http://dx.doi.org/10.1115/1.2464145.
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Linear cascade measurements for the aerodynamic performance of a family of three transonic, high-pressure (HP) turbine blades have been presented previously by the authors. The airfoils were designed for the same inlet and outlet velocity triangles but varied in their loading distributions. The previous papers presented results for the design incidence at various exit Mach numbers, and for off-design incidence at the design exit Mach number of 1.05. Results from the earlier studies indicated that by shifting the loading towards the rear of the airfoil an improvement in the profile loss performance of the order of 20% could be obtained near the design Mach number at design incidence. Measurements performed at off-design incidence, but still at the design Mach number, showed that the superior performance of the aft-loaded blade extended over a range of incidence from about −5.0deg to +5.0deg relative to the design value. For the current study, additional measurements were performed at off-design Mach numbers from about 0.5 to 1.3 and for incidence values of −10.0deg, +5.0deg, and +10.0deg relative to design. The corresponding Reynolds numbers, based on outlet velocity and true chord, varied from roughly 4×105 to 10×105. The measurements included midspan losses, blade loading distributions, and base pressures. In addition, two-dimensional Navier–Stokes computations of the flow were performed to help in the interpretation of the experimental results. The results show that the superior loss performance of the aft-loaded profile, observed at design Mach number and low values of off-design incidence, does not extend readily to off-design Mach numbers and larger values of incidence. In fact, the measured midspan loss performance for the aft-loaded blade was found to be inferior to, or at best equal to, that of the baseline, midloaded airfoil at most combinations of off-design Mach number and incidence. However, based on the observations made at design and off-design flow conditions, it appears that aft-loading can be a viable design philosophy to employ in order to reduce the losses within a blade row provided the rearward deceleration is carefully limited. The loss performance of the front-loaded blade is inferior or at best equal to that of the other two blades for all operating conditions.
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Li, Bei, Yang Liu, Mrinal K. Sen, and Zhiming Ren. "Time-space-domain mesh-free finite difference based on least squares for 2D acoustic-wave modeling." GEOPHYSICS 82, no. 4 (2017): T143—T157. http://dx.doi.org/10.1190/geo2016-0464.1.
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Finite-difference (FD) methods approximate derivatives through a weighted summation of function values from neighboring nodes. Traditionally, these neighboring nodes are assumed to be distributed regularly, such as in square or rectangular lattices. To improve geometric flexibility, one option is to develop FD in a mesh-free discretization, in which scattered nodes can be placed suitably with respect to irregular boundaries or arbitrarily shaped anomalies without coordinate transformation or forming any triangles or tetrahedra, etc. These mesh-free FDs have had successful applications, especially in computational geoscience. However, they are all space-domain FD schemes, in which FD coefficients are derived by approximating spatial derivatives individually in the space domain. For acoustic-wave modeling, it has been proven that space-domain FD methods normally have higher dispersion error than time-space-domain FD methods, which determine FD coefficients by approximating the time-space-domain dispersion relation. Now, we have developed a time-space-domain mesh-free FD based on minimizing the absolute error of the dispersion relation by least-squares (LS) for 2D acoustic-wave modeling. The matrix used to solve for FD coefficients in our method is determined by the spatial distribution of the nodes in a local FD stencil, whereas the temporal step size and velocity information are considered in the right side of the linear system. This feature of considering both spatial and temporal effects allows our proposed mesh-free LS-based FD to obtain greater temporal accuracy adaptive to different Courant-Friedrichs-Lewy parameters than pure space-domain mesh-free FDs. Under several 2D acoustic scenarios, the advantage was proven by comparing our method with radial-basis-function-generated FD, which is one of the most popular mesh-free FDs and has been applied in elastic wave modeling.
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Бойко, Людмила Георгиевна, Александр Евгеньевич Демин та Наталия Владимировна Пижанкова. "МЕТОД РАСЧЁТА ТЕРМОГАЗОДИНАМИЧЕСКИХ ПАРАМЕТРОВ ТУРБОВАЛЬНОГО ГАЗОТУРБИННОГО ДВИГАТЕЛЯ НА ОСНОВЕ ПОВЕНЦОВОГО ОПИСАНИЯ ЛОПАТОЧНЫХ МАШИН. ЧАСТЬ II. ОПРЕДЕЛЕНИЕ ПАРАМЕТРОВ СТУПЕНЕЙ И МНОГОСТУПЕНЧАТЫХ КОМПРЕССОРОВ". Aerospace technic and technology, № 1 (7 березня 2019): 18–28. http://dx.doi.org/10.32620/aktt.2019.1.02.
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Gas Turbine Engine (GTE) operating characteristics such as thrust (or power), specific fuel consumption and other cycle parameters on different regimes, can be determined by engine modeling and applying correspondent calculation method. Its accuracy is the function of the engine’s element maps definition precision. So these maps representations influence for engines investigation results significantly. Main points and equation system for engine performances calculation method were represented in Part I of this article. The method gives an opportunity for the flow path thermodynamical parameters and engine integral values analyzing by using multistage axial blade machines blade-to-blade descriptions. The compressor and gas turbine and parameters are getting by special program modules, adding to the engine operating characteristics investigation program complex. These modules use the flow path and cascade middle radius geometrical parameters as the data for calculation. The goal of this article is the representation of the method for axial stages and multistage compressors performances definition. The calculation technique is based on one-dimensional (1D) multistage axial compressor flow description. Proposed 1D flow analysis method allows to get the multistage axial compressor maps taking into account the blade-to-blade gaps flow bleeding and by-pass. The method including is founded on the thermal and gas dynamic equations and turbomachinery theoretical dependences and empirical functions for losses and deviation angles determination. Besides, the representing method allows to calculate gas dynamic parameters, velocity triangles, angles of attack, evaluate their deviations from optimal values, hydraulic losses. Also, it can show accordance of stages working on different regimes, find the stage, which is a reason for compressor instability, and stall margin. This method can be used in GTE mathematic simulation, founded on blade-to-blade description multistage blade machines or also in multistage compressor designing. The proposed method gives the opportunity to control the stator variable vanes stagger angles control and to analyze its influence for stage and multistage compressor gas dynamic parameters and maps.
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Bartenev, Ivan, and Aleksandr Petkov. "ANALYSIS OF STRUCTURES AND WORK PROCESSES OF TECHNICAL FACILITIES FOR PREVENTION AND SUPPRESSION OF FOREST FIRES BY SOIL." Actual directions of scientific researches of the XXI century: theory and practice 8, no. 2 (2020): 5–11. http://dx.doi.org/10.34220/2308-8877-2020-8-2-5-11.
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The analysis of designs of domestic and foreign ground-throwing machines and conducted research on extinguishing a forest grass-roots fire by throwing soil. It is established that for carrying out high-quality preventive and forest fire works, it is advisable to use technical means that combine active and passive working bodies in their design. This will allow combining the process of pre-treatment of soil and further release of loosened soil in a given direction, as well as significantly increase the efficiency of the technological process of creating mineralized strips. Based on the mathematical model, the working surfaces of the soil-laying machine are represented as a set of elementary triangles with vertex coordinates and the nature of soil movement is studied. The main part of the flying soil (about 70 %) settles in the band from 1.5 to 3.0 m from the border of the machine. However, part of the ground gets a high initial velocity and such an angle of release that it reaches a distance of 20 to 40 m. To study the movement of the elements of the ground-thrower, equations of motion of the mechanical system in the form of Lagrange equations of the second kind are compiled. It was found that when the values of the depth of the casing-Ripper are from 0.25 to 0.3 m, the best indicators of the range of soil discharge and productivity are observed (20 m and 0.07 m3 / s, respectively), and the power consumption is in the permissible range (17 kW). It is concluded that the ground-throwing equipment should be considered only as part of a combined machine that will allow you to remove the forest floor from the path of the unit, preventing its release into the fire zone, and protecting the working bodies of the unit from the root system of trees. The highly efficient design of the unit with technical solutions is proposed, which allows performing work on stopping and localizing fire.
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Bin Ramli, Mohd Syaifullah, Abdul Basit, Ku Zilati Ku Shaari, and Lau Kok Keong. "Study of the Effect of Surface Roughness on Droplet Spreading Behavior Using CFD Modeling." Applied Mechanics and Materials 625 (September 2014): 378–81. http://dx.doi.org/10.4028/www.scientific.net/amm.625.378.
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Water droplet spreading has been simulated at impact velocity of 3.0 m/s, 1.5 m/s and 0.5 m/s on surfaces with texture of ‘triangle’, ‘square’, ‘curve’ as well as smooth surface of aluminum. Higher impact velocity induced the droplet to spread faster and has a bigger diameter. At high impact velocity, spreading factor cannot be determined due to splashing and droplet break ups. In addition, at 1.5 m/s the phenomenon of splashing was found to be almost absent except on the surface with ‘square’ texture. ‘Square’ surface tends to splash earlier compared to other surfaces and is followed by ‘triangle’, ‘curve’ and smooth surface. At low impact velocity, the smooth surface has the highest spreading factor and followed by ‘triangle’, ‘square’ and ‘curve’ surface.
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Pan, Minqiang, Yong Tang, Hao Yu, and Hongqing Chen. "Modeling of velocity distribution among microchannels with triangle manifolds." AIChE Journal 55, no. 8 (2009): 1969–82. http://dx.doi.org/10.1002/aic.11817.
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Iwahashi, Yohei, Masaki Miyazato, Masaaki Miyajima, et al. "Extension of Stacking Faults in 4H-SiC pn Diodes under a High Current Pulse Stress." Materials Science Forum 897 (May 2017): 218–21. http://dx.doi.org/10.4028/www.scientific.net/msf.897.218.
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We investigated the expansion of stacking faults (SFs) under a high current pulse stress in detail. In situ observations showed bar-shaped SFs and two types of triangle SFs with different nucleation sites. The calculated partial dislocation velocity of the bar-shaped SFs was four times faster than that of the triangle SFs. The temperature dependence of the partial dislocation velocity was used to estimate activation energies of 0.23±0.02 eV for bar-shaped SFs and 0.27±0.05 eV for triangle SFs. We also compared the electrical characteristics before and after the stress. The forward voltage drop slightly increased by 0.05 V, and the leakage current did not increase.
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Beiner, L. "Kinematics of a n–bay triangle–triangle variable geometry truss manipulator." Robotica 10, no. 3 (1992): 263–67. http://dx.doi.org/10.1017/s0263574700007992.
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SUMMARYVariable geometry truss manipulators (VGTM) are static trusses where the lengths of some members can be varied, allowing one to control the position of the free end relative to the fixed one. This paper deals with a planar VGTM consisting of a n–bay triangle-triangle truss with one variable length link (i.e. one DOF) per bay. Closed-form solutions to the forward, inverse, and velocity kinematics of a 3-DOF version of this VGTM are presented, while the forward and inverse kinematics of an n–DOF (redundant) one are solved by a recursive and an iterative method, respectively. A numerical example is presented.
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Zhu, Jianjun, Haiwen Zhu, Guangqiang Cao, et al. "A New Mechanistic Model To Predict Boosting Pressure of Electrical Submersible Pumps Under High-Viscosity Fluid Flow with Validations by Experimental Data." SPE Journal 25, no. 02 (2019): 744–58. http://dx.doi.org/10.2118/194384-pa.
Full textAbstract:
Summary As the second most widely used artificial-lift method in petroleum production (and first in accumulative production), electrical submersible pumps (ESPs) increase flow rates by converting kinetic energy to hydraulic pressure. ESPs are routinely characterized with water flow, and water performance curves are provided by the manufacturers (catalog curves) for designing ESP-based artificial-lift systems. However, the properties of hydrocarbon fluids are very different from those of water, especially the dynamic viscosities, which can significantly alter the ESP performance. Most of the existing methods to estimate ESP boosting pressure under high-viscosity fluid flow involve a strong empirical nature, and are derived by correlating experimental/field data with correction factors (e.g., Hydraulic Institute Standards 1955). A universally valid mechanistic model to calculate the ESP boosting pressure under viscous fluid flow is not yet available. In this paper, a new mechanistic model accounting for the viscosity effect of working fluids on ESP hydraulic performance is proposed, and it is validated with a large database collected from different types of ESPs. The new model starts from the Euler equations for characterizing centrifugal pumps, and introduces a conceptual best-match flow rate QBM, at which the outlet flow direction of the impeller matches the designed flow direction. The mismatch of velocity triangles, resulting from the varying liquid-flow rates, is used to derive the recirculation losses. Other head losses caused by flow-direction change, friction, leakage flow, and other factors. are incorporated into the new model as well. QBM is obtained by matching the predicted H-Q performance curve of an ESP with the catalog curves. Once QBM is determined, the ESP hydraulic head under viscous-fluid-flow conditions can be calculated. The specific speed (NS) of the studied ESPs in this paper ranges from 1,600 to 3,448, including one radial-type ESP and two mixed-type designs. The model-predicted ESP boosting pressure with water flow is found to match the catalog curves well if QBM is properly tuned. With high-viscosity fluid presence, the model predictions of ESP boosting pressure also agree well with the corresponding experimental data. For most calculation results within medium to high flow rates, the model prediction error is less than 15%. Unlike the empirical correlations that take experimental data points as inputs, the mechanistic model in this study does not require entering any experimental data, but can predict ESP boosting pressure under viscous fluid flow with a reasonable accuracy.
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Li, Guan Nan, Hui Ying Dong, and Hong Li Xu. "Triangle Formation Control of Multi-AUVs with Communication Constraints." Applied Mechanics and Materials 596 (July 2014): 631–35. http://dx.doi.org/10.4028/www.scientific.net/amm.596.631.
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Aimed at solving the problem of multi-AUVs formation control, an analysis has been made on a triangle formation based on leader-follower construction, with a multi-AUVs formation controller designed with communication constraints taken into account. The desired velocity of the follower is the resultant velocity of three component velocities, each of which has different function. The convergence of the proposed controller is proved by establishing an objective function that can represents the status of the formation. Simulation experiments are carried out to demonstrate the proposed controller is effective.
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Zhang, Yu Shu. "Analysis and Calculation of Transmission Ratio of Simpson Planetary Gear Mechanism Based on Velocity Graphic Method." Advanced Materials Research 889-890 (February 2014): 532–36. http://dx.doi.org/10.4028/www.scientific.net/amr.889-890.532.
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The paper summarizes the principle of applying velocity graphic method to analyze Simpson planetary gear mechanism, which provides guidance for analysis procedure. The movement of each element in the mechanism can be intuitively understood through drawing the linear velocity vectors of three constant velocity points. The similar triangle principle is used to calculated transmission ratio of each transmission scheme in the linear velocity vector diagram, and the correctness of the analysis method and process is verified by the transmission ratio calculated by velocity graphic method and analytic method.
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Monteagudo, Jorge E. P., and Abbas Firoozabadi. "Control-Volume Model for Simulation of Water Injection in Fractured Media: Incorporating Matrix Heterogeneity and Reservoir Wettability Effects." SPE Journal 12, no. 03 (2007): 355–66. http://dx.doi.org/10.2118/98108-pa.
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Summary The control-volume discrete-fracture (CVDF) model is extended to incorporate heterogeneity in rock and in rock-fluid properties. A novel algorithm is proposed to model strong water-wetting with zero capillary pressure in the fractures. The extended method is used to simulate:oil production in a layered faulted reservoir,laboratory displacement tests in a stack of matrix blocks with a large contrast in fracture and matrix capillary pressure functions, andwater injection in 2D and 3D fractured media with mixed-wettability state. Our results show that the algorithm is suitable for the simulation of water injection in heterogeneous porous media both in water-wet and mixed-wettability states. The novel approach with zero fracture capillary and nonzero matrix capillary pressure allows the proper prediction of sharp fronts in the fractures. Introduction This work is focused on the numerical treatment of two main physical aspects of multiphase flow in fractured porous media: heterogeneity in rock-fluid properties and reservoir wettability. In a previous work (Monteagudo and Firoozabadi 2004), a CVDF method was used to discretize the system of equations governing water injection in fractured media with strong-water-wettability state and homogeneous matrix and rock-fluid properties. The method was restricted to a finite contrast in matrix-fracture capillary pressure. In this work, we extend the CVDF model for simulation of water injection in fractured media comprised of heterogeneous rocks and wettability conditions from strong-water-wetting to mixed-wetting conditions. We also present a formulation for infinite contrast in capillary pressures of matrix and fractures (zero capillary pressure in the fracture and finite capillary pressure in the matrix). The control volume (CV) method, first proposed by Baliga and Patankar (1980), is a finite-volume formulation over dual cells (CVs) of a Delaunay mesh. It is locally conservative and suited for unstructured grids. It has been widely employed for the simulation of multiphase flow in porous media (Monteagudo and Firoozabadi 2004; Verma 1996; Helmig 1997; Helmig and Huber 1998; Bastian et al. 2000; Geiger et al. 2003) and the convergence of the method for two-phase immiscible flow in porous medium has already been proved (Michel 2003). Numerical treatment of heterogeneity in the framework of the CV method has been extensively studied in the past (Edwards 2002; Edwards and Rogers 1998; Prevost 2000; Aavatsmark et al. 1998a, b). Nevertheless, those works have focused on absolute permeability heterogeneity and anisotropy in single-phase flow. The main concern in those works is the use of full tensor permeability and the accurate generation of streamlines (required by the streamline numerical method). It is well known that the standard CV method produces inaccurate velocity fields around the interfaces of heterogeneous media as the contrast in permeability is increased (Durlofsky 1994). In the standard CV method, Delaunay triangles are locally homogeneous and the polygonal CV cell may be heterogeneous (see Fig. 1a). For accurate streamlines, several authors (Verma 1996; Edwards 2002; Edwards and Rogers 1998; Prevost 2000; Aavatsmark et al. 1998a) have proposed that the polygonal CV cell must be locally homogeneous, implying heterogeneous Delaunay triangles (see Fig. 1b). The latter configuration, however, generates additional problems in the simulation of multiphase flow in porous media. Basically, from mesh generation standpoint, it may not be possible to generate an unstructured mesh where the boundaries of the CV median-dual cell conform to heterogeneous interfaces in the domain. Conforming mesh is important for the discrete-fracture approach. Therefore, it would be necessary to first generate a standard CV cell mesh, and later a homogenization procedure would be required to obtain CV cells with constant permeability. The homogenization or upscaling of permeability is somehow possible, but the same is not true for rock-fluid properties; most challenging is capillary pressure with different endpoints. Therefore, the approach with the homogeneous CV cell may be suitable for single-phase simulation where rock-fluid interactions are not part of the problem. However, rock-fluid interactions have to be taken into account for simulation of multiphase flow in fractured porous medium. Frequently, capillary pressure is disregarded in two-phase flow simulations; however, capillary pressure is of importance for simulation of multiphase flow in fractured porous media (Monteagudo and Firoozabadi 2004; Karimi-Fard and Firoozabadi 2003). Predictions of flow pattern and oil recovery may be severely affected if capillary pressure effect is neglected.
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Su, Mingxiao, Xiyun Jiao, Jiang Li, Shuyu Wu, and Tianao Wu. "Accuracy and Reliability Analysis of Pipe Irrigation Metering Device for Sandy Water Source." Water 13, no. 7 (2021): 947. http://dx.doi.org/10.3390/w13070947.
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Sandy water sources are widely distributed and are important for agricultural development. However, no explicit result has been achieved in the research of the accuracy and reliability of pipeline metering devices as well as flow rate measurement objects (water or water–sand) of different metering devices in the process of pipelines conveying muddy water. In this study, seven kinds of sediment concentration gradients, C0–C6 (0.2–7.19%), and three different flow velocities (1.0 m/s, 1.25 m/s, 1.5 m/s) were set up, and a comparison measuring method was used to compare the flow values of three kinds of metering device (electromagnetic flowmeter, ultrasonic flowmeter and water meter) with a right triangle weir. The accuracy and reliability of the metering device were obtained by analyzing the change law of the relative error between each metering device and the right triangle weir under different flow velocities and different sediment concentrations, and the flow rate measurement objects of each metering device were finally clarified. The relative error between the electromagnetic flowmeter and right triangle weir decreased gradually with the increase in the flow velocity when the sediment concentration was constant. The maximum difference of the relative error between the electromagnetic flowmeter and the right triangle weir was 2.53% when the flow velocity was constant. Additionally, the minimum differences of the relative errors of the ultrasonic flowmeter and water meter were 2.67% and 6.90%, respectively. The measured flow law of the electromagnetic flowmeter was more in line with the measured flow law of the water–sand mixture measured by the right triangle weir. However, the relative errors of water and water–sand measured by the ultrasonic flowmeter and water meter fluctuate greatly, which does not accord with the law of muddy water measured by the right triangle weir. The results showed that the electromagnetic flowmeter has the best reliability among the three metering devices, and the accuracy can be improved by calibration before use or increasing the flow velocity of the pipe network. Under the sand grading used in this study, the electromagnetic flowmeter was recommended to measure the flow rate of pipe irrigation for sandy water sources in this paper.