Bernoulli integral and conservation of velocity circulation in polarizing or magnetizing fluid

1978 ◽  
Vol 13 (3) ◽  
pp. 474-477
Author(s):  
V. B. Gorskii
Keyword(s):  
Velocity Circulation ◽  
Bernoulli Integral

On uniqueness and solvability in the linearized two-dimensional problem of a supercritical stream about a surface-piercing body

1995 ◽  
Vol 450 (1939) ◽  
pp. 233-253 ◽  
Keyword(s):  
Free Surface ◽  
Linear Relation ◽  
Existence Of Solutions ◽  
Surface Elevation ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Free Surface Elevation ◽  
Unique Existence ◽  
Velocity Circulation ◽  
Well Posed

Uniqueness and solvability theorems are proved for a well-posed formulation of the two-dimensional Neumann-Kelvin problem (the modified Neumann-Kelvin problem) in the case, when a body is partly immersed in a supercritical stream. Uniqueness is provided by two supplementary conditions which prescribe (i) additional flux at infinity downstream due to presence of body and (ii) a linear relation between the free-surface elevation at stern point and the velocity circulation along wetted contour. Two versions of source method are developed to find a solution. The first version is simpler, but it fails for some irregular values of the body’s velocity. In the second ver­sion complex sources’ strengths are used, avoiding irregular values and establishing the unique existence of solutions.

Characteristic Analysis on Mountain-Valley Wind in Deep Valley

2012 ◽  
Vol 610-613 ◽  
pp. 817-824
Author(s):  
Wen Yong Wang ◽  
Nan Chen ◽  
Xiao Juan Ma
Keyword(s):  
Wind Speed ◽  
Measured Data ◽  
Characteristic Analysis ◽  
Valley Wind ◽  
Average Wind Speed ◽  
Mountain Valley ◽  
Average Wind ◽  
Slope Wind ◽  
Velocity Circulation ◽  
Thermodynamic Effects

Taking the actual measured data and the simulating result from WRF(Weather Research & Forecasting)/CALMET numerical model, analysing the air flow field in the industrial park in some valley of northern Sichuan Province, it shows that the valley has the mountain-valley wind formed by the topographical thermodynamic effects, and the characters of mountain-valley wind change with season. In January in winter, the valley wind appears at 8:30 in the morning, and prevails after 2 hours transition. The wind strength (wind velocity, circulation height and thickness) is the strongest at about 14:00. The valley wind lasts about 7 hours, and then changes into the mountain wind at 17:30. After 3.5 hours, at 21:00, the mountain wind prevails and lasts 11.5 hours to 8:30 in the next morning. In July in summer, the valley wind appears at 6:30 in the morning. Through 1.5 hours transition, the valley wind prevails at 8:00 and becomes the strongest at 14:00. The valley wind lasts about 10.5 hours and begins to change into the mountain wind at 19:00 in 3 hours. From 22:00 to 6:30 in the next morning, the slope wind prevails and lasts about 8.5 hours. In winter, the thickness for valley wind is bout 100~300m with the average wind speed 1.5~4.0m/s and the thickness for mountain wind is 50~200m with average wind speed 1.5~3.0m/s and circulating sphere height 600~800m. In summer, the valley wind thickness is about 200~500m with average wind speed 2.0~7.0m/s and the mountain wind thickness is about 150~400m with average wind speed 1.5~5m/s and circulation layer height 600~800m. Since the orientation of mountains is different at the both sides of valley, the time and the strength for the mountains receiving the solar radiation are different, the regulation and the characters for mountain-valley wind appearing and disappearing are also different.

scholarly journals The Effect of Angular Momentum and Ostrogradsky-Gauss Theorem in the Equations of Mechanics

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Mathematical Models ◽  
Conservation Laws ◽  
Rarefied Gas ◽  
Classical Mechanics ◽  
Gauss Theorem ◽  
The Media ◽  
Velocity Circulation ◽  
The Times ◽  
The Many ◽  
Definition Of

There are many experimental facts that currently cannot be described theoretically. A possible reason is bad mathematical models and algorithms for calculation, despite the many works in this area of research. The aim of this work is to clarificate the mathematical models of describing for rarefied gas and continuous mechanics and to study the errors that arise when we describe a rarefied gas through distribution function. Writing physical values conservation laws via delta functions, the same classical definition of physical values are obtained as in classical mechanics. Usually the derivation of conservation laws is based using the Ostrogradsky-Gauss theorem for a fixed volume without moving. The theorem is a consequence of the application of the integration in parts at the spatial case. In reality, in mechanics and physics gas and liquid move and not only along a forward path, but also rotate. Discarding the out of integral term means ignoring the velocity circulation over the surface of the selected volume. When taking into account the motion of a gas, this term is difficult to introduce into the differential equation. Therefore, to account for all components of the motion, it is proposed to use an integral formulation. Next question is the role of the discreteness of the description of the medium in the kinetic theory and the interaction of the discreteness and "continuity" of the media. The question of the relationship between the discreteness of a medium and its description with the help of continuum mechanics arises due to the fact that the distances between molecules in a rarefied gas are finite, the times between collisions are finite, but on definition under calculating derivatives on time and space we deal with infinitely small values. We investigate it

scholarly journals Blade Tip-Vortices of a Four-Bladed Rotor with Axial Inflow

2020 ◽  
Vol 65 (4) ◽  
pp. 1-13
Author(s):  
Andreas Goerttler ◽  
Johannes N. Braukmann ◽  
C. Christian Wolf ◽  
Anthony D. Gardner ◽  
Markus Raffel
Keyword(s):  
Particle Image ◽  
Test Facility ◽  
Vortex System ◽  
Tip Vortices ◽  
Image Velocimetry ◽  
Swirl Velocity ◽  
Blade Tip ◽  
Velocity Circulation ◽  
Bladed Rotor ◽  
German Aerospace

The vortex system of four rotating and pitching DSA-9A blades was examined numerically and experimentally. Numerical computations were performed using German Aerospace Center (DLR)'s finite-volume solver TAU and were validated against experimental data gathered using particle image velocimetry carried out at the rotor test facility (RTG) in Göttingen. Algorithms deriving the vortex position, swirl velocity, circulation, and core radius were implemented. Hover-like conditions with a fixed blade pitch were analyzed giving further physical insights of the static vortex system. These results are used to understand the vortex development for the unsteady pitching conditions, which can be described as a superpositioning of static vortex states. The use of a zonal detached-eddy simulations approach improved physical modeling of the vortex development by resolving finer scales than URANS. Trimmed cases agree well with differences less than 0.5% in the circulation and swirl velocity.

Spectra of velocity circulation in the surface layer of the atmosphere

1988 ◽  
Vol 42 (1-2) ◽  
pp. 137-143 ◽  
Author(s):  
B. M. Koprov ◽  
G. V. Azizyan ◽  
V. V. Kalugin
Keyword(s):  
Surface Layer ◽  
Velocity Circulation

Analytic and Experimental Investigation of Dihedral Configurations of Three-Winglet Planforms

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
David S. Miklosovic
Keyword(s):  
Aspect Ratio ◽  
Lift Coefficient ◽  
Pitching Moment ◽  
Lattice Method ◽  
Vortex Lattice Method ◽  
Moment Coefficient ◽  
Velocity Circulation ◽  
Low Speed Wind Tunnel ◽  
Experimental Effort ◽  
Good Agreement

An analytic and experimental effort was undertaken to assess the effectiveness and efficiency of three winglets mounted chordwise to the tip of a rectangular wing. The winglets, with an aspect ratio of 4.6, were mounted on a half-span wing having an effective aspect ratio of 6.29. 13 configurations of varying dihedral arrangements were analyzed with a vortex lattice method and tested in a low-speed wind tunnel at a Reynolds number of 600,000. While the analytic method provided fair agreement with the experimental results, the predicted trends in lift, drag, and (to a lesser degree) pitching moment were in good agreement. The analytic distributions of wake velocity, circulation, and downwash angle verified that highly nonplanar configurations tended to reduce and diffuse the regions of highest circulation and to create more moderate downwash angles in the wake. This was manifest as an overall drag reduction. More specifically, the results showed that the winglets could be placed in various optimum orientations to increase the lift coefficient as much as 65% at the same angle of attack, decrease the drag coefficient as much as 54% at the same lift coefficient, or improve the maximum L∕D by up to 57%. The most dramatic findings from this study show that positioning the winglet dihedral angles had the result of adjusting the magnitude and slope of the pitching moment coefficient. These observations suggest that multiple winglet dihedral variations may be feasible for use as actively controlled surfaces to improve the performance of aircraft at various flight conditions and to “tune” the longitudinal stability characteristics of the configuration.

Design and Test for High Specific Speed Mixed Flow Pump with Volute

2011 ◽  
Vol 354-355 ◽  
pp. 669-673
Author(s):  
Xian Fang Wu ◽  
Hou Lin Liu ◽  
Ming Gao Tan ◽  
Hong Hui Li
Keyword(s):  
Cross Sections ◽  
Flow Analysis ◽  
Maximum Efficiency ◽  
Blade Angle ◽  
Mixed Flow ◽  
Commercial Code ◽  
Hydraulic Design ◽  
Velocity Circulation ◽  
Specific Speed ◽  
Flow Pump

The characteristics and research actuality on mixed flow pumps are introduced simplely. A mixed flow pump with volute as diffusion part is designed and its specific speed is 556.8. The axial velocity circulation and blade angle variety with linearity distribution are used to deisign the impeller. The fixed diffeuser between impeller and volute is deigned by arc airfoil.The cross sections of volute are all asymmetry. The commercial code FLUENT is applied to simulate the inner flow in the mixed flow pump and its energy characteristics are predicted according to the simulation results. The inner flow analysis indicates that the flow in the pump is good and the characteristic prediction shows that the pump performance can meet the design demand. The experiment test of the pump are done. When the blade angle is about 0°, the maximum efficiency of the pump is up to 85.76% and the actual efficiency at design point is about 3% higher than demand efficiency. The study fruits can instruct the hydraulic design of higher specific speed mixed flow pump with volute as diffusion part.

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