Addendum to Sphere Theorem on the Stokes Equation for Three-Dimensional Viscous Flow

1995 ◽  
Vol 64 (9) ◽  
pp. 3581-3582 ◽  
Author(s):  
Hidenori Hasimoto
Keyword(s):  
Viscous Flow ◽  
Stokes Equation ◽  
Three Dimensional ◽  
Sphere Theorem ◽  
The Stokes Equation

Viscous flow around three-dimensional macroscopic cavities in a granular material

2021 ◽  
Vol 931 ◽  
Author(s):  
Osamu Sano ◽  
Timir Karmakar ◽  
G.P. Raja Sekhar
Keyword(s):  
Granular Material ◽  
Viscous Flow ◽  
Stokes Equation ◽  
Three Dimensional ◽  
Volume Flow ◽  
The Other ◽  
Brinkman Equation ◽  
Local Enhancement ◽  
Reasonable Estimate ◽  
The Stokes Equation

Viscous flow around spherical macroscopic cavities in a granular material is investigated. The Stokes equation inside and the Darcy–Brinkman equation outside the cavities are considered. In particular, the interaction of two equally sized cavities positioned in tandem is examined in detail, where the asymptotic effect of the other cavity is taken into account. The present analysis gives a reasonable estimate on the volume flow into the cavity and the local enhancement of stresses. This is applicable to predict the microscale waterway formation in that material, onset of landslides, collapse of cliffs and river banks, etc.

scholarly journals A tridimensional model for the motion of nanobots at high viscosity coeflcient environment based on Navier-Stokes’ Equation, by applying Oseen’s approximation

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Alireza Jorkesh ◽  
Amir Hossein Ghaffari ◽  
Amir Abolfazleh Suratgar ◽  
Mahmoud Dehghan Afify
Keyword(s):  
Stokes Equation ◽  
Three Dimensional ◽  
High Viscosity ◽  
Navier Stokes ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Navier Stokes Equation ◽  
The Stokes Equation

Abstract Till now, various models of the motion of nanobots have been submitted; the pioneer models, in spite of being exact in mathematics, had their own kind of problems. The most recent challenge is to describe a model whose attitude can be practical so that these motions can be estimated. Considering the massive uses of nanobots, the kinds of motions and velocities of these very small robots need to be studied in a more accurate way. In this essay, we tried to develop a three-dimensional model. The three dimensional model is based on 7 spheres and 6 arms and describes a kind of movement requiring 2 spheres at each arm. The velocity of each kind has also been evaluated. Furthermore, two kinds of three-dimensional movements have been issued and compared as well. That will result in the simplicity of the equations. By applying Oseen’s approximation in the Stokes’ equation, the velocity in various media has been calculated and modulated.

Three-dimensional thermochemical nonequilibrium viscous flow over blunt bodies with catalytic surface

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 626-636
Author(s):  
S. Peigin ◽  
V. Kazakov ◽  
M.-C. Druguet ◽  
S. Seror ◽  
D. E. Zeitoun
Keyword(s):  
Viscous Flow ◽  
Three Dimensional ◽  
Catalytic Surface ◽  
Blunt Bodies

Effects of Inlet Distortion on the Flow Field in a Transonic Compressor Rotor

1996 ◽  
Author(s):  
Chunill Hah ◽  
Douglas C. Rabe ◽  
Thomas J. Sullivan ◽  
Aspi R. Wadia
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Viscous Flow ◽  
Total Pressure ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Aerodynamic Loss ◽  
Transonic Compressor ◽  
Inlet Distortion ◽  
Compressor Rotor

The effects of circumferential distortions in inlet total pressure on the flow field in a low-aspect-ratio, high-speed, high-pressure-ratio, transonic compressor rotor are investigated in this paper. The flow field was studied experimentally and numerically with and without inlet total pressure distortion. Total pressure distortion was created by screens mounted upstream from the rotor inlet. Circumferential distortions of 8 periods per revolution were investigated at two different rotor speeds. The unsteady blade surface pressures were measured with miniature pressure transducers mounted in the blade. The flow fields with and without inlet total pressure distortion were analyzed numerically by solving steady and unsteady forms of the Reynolds-averaged Navier-Stokes equations. Steady three-dimensional viscous flow calculations were performed for the flow without inlet distortion while unsteady three-dimensional viscous flow calculations were used for the flow with inlet distortion. For the time-accurate calculation, circumferential and radial variations of the inlet total pressure were used as a time-dependent inflow boundary condition. A second-order implicit scheme was used for the time integration. The experimental measurements and the numerical analysis are highly complementary for this study because of the extreme complexity of the flow field. The current investigation shows that inlet flow distortions travel through the rotor blade passage and are convected into the following stator. At a high rotor speed where the flow is transonic, the passage shock was found to oscillate by as much as 20% of the blade chord, and very strong interactions between the unsteady passage shock and the blade boundary layer were observed. This interaction increases the effective blockage of the passage, resulting in an increased aerodynamic loss and a reduced stall margin. The strong interaction between the passage shock and the blade boundary layer increases the peak aerodynamic loss by about one percent.

Factors Affecting Measured Axial Compressor Tip Clearance Vortex Circulation

1995 ◽  
Vol 117 (3) ◽  
pp. 487-490 ◽  
Author(s):  
S. A. Khalid
Keyword(s):  
Viscous Flow ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Tip Clearance ◽  
Radial Transport ◽  
Factors Affecting ◽  
Blade Tip ◽  
Tip Clearance Vortex ◽  
The Relationship ◽  
Principal Contributor

The relationship between turbomachinery blade circulation and tip clearance vortex circulation measured experimentally is examined using three-dimensional viscous flow computations. It is shown that the clearance vortex circulation one would measure is dependent on the placement of the fluid contour around which the circulation measurement is taken. Radial transport of vorticity results in the magnitude of the measured clearance vortex circulation generally being less than the blade circulation. For compressors, radial transport of vorticity shed from the blade tip in proximity to the endwall is the principal contributor to the discrepancy between the measured vortex circulation and blade circulation. Further, diffusion of vorticity shed at the blade tip toward the endwall makes it impossible in most practical cases to construct a fluid contour around the vortex that encloses all, and only, the vorticity shed from the blade tip. One should thus not expect agreement between measured tip clearance vortex circulation and circulation around the blade.

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