General Solutions of the Stokes Equations

2012 ◽  
pp. 149-176
Keyword(s):  
Stokes Equations ◽  
General Solutions

scholarly journals Unsteady stokes equations: Some complete general solutions

2004 ◽  
Vol 114 (2) ◽  
pp. 203-213 ◽  
Author(s):  
A. Venkatlaxmi ◽  
B. S. Padmavathi ◽  
T. Amaranath
Keyword(s):  
Stokes Equations ◽  
General Solutions ◽  
Unsteady Stokes Equations

scholarly journals About general solutions of Euler’s and Navier-Stokes equations

2019 ◽  
pp. 190-193
Author(s):  
V. I. Rozumniuk
Keyword(s):  
General Solution ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Fundamental Problem ◽  
Diffusion Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
General Solutions ◽  
And Diffusion

Constructing a general solution to the Navier-Stokes equation is a fundamental problem of current fluid mechanics and mathematics due to nonlinearity occurring when moving to Euler’s variables. A new transition procedure is proposed without appearing nonlinear terms in the equation, which makes it possible constructing a general solution to the Navier-Stokes equation as a combination of general solutions to Laplace’s and diffusion equations. Existence, uniqueness, and smoothness of the solutions to Euler's and Navier-Stokes equations are found out with investigating solutions to the Laplace and diffusion equations well-studied.

scholarly journals On the flow in an annulus surrounding a whirling cylinder

1976 ◽  
Vol 75 (1) ◽  
pp. 173-191 ◽  
Author(s):  
Christopher Brennen
Keyword(s):  
Stokes Equations ◽  
Reynolds Numbers ◽  
Journal Bearings ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
General Solutions ◽  
Rotor Systems ◽  
Dynamic Forces

When fluid in an annulus between two cylinders is set in motion by whirling movements of one or both of the cylinders, dynamic forces are imposed by the fluid on the cylinders. Knowledge of these forces is frequently important, indeed often critical, to the engineer designing rotor systems or journal bearings. Quite general solutions of the Navier-Stokes equations are presented for this problem and are limited only by restrictions on the amplitude of the whirl motion. From these solutions, the forces are derived under a wide variety of circumstances, including large and small annular widths, high and low Reynolds numbers and with and without a mean flow created by additional net rotation of one or both of the cylinders.

scholarly journals General solutions of the Stokes equations and their applications

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1100701-1100702 ◽  
Author(s):  
T. Amaranath
Keyword(s):  
Stokes Equations ◽  
General Solutions

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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