A generalized Clebsch transformation leading to a first integral of Navier–Stokes equations

2016 ◽  
Vol 380 (40) ◽  
pp. 3258-3261 ◽  
Author(s):  
M. Scholle ◽  
F. Marner
Keyword(s):  
Stokes Equations ◽  
First Integral ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Exact Solution of 3D Navier–Stokes Equations

2020 ◽  
pp. 306-313
Author(s):  
Alexander V. Koptev
Keyword(s):  
Exact Solution ◽  
Fluid Flow ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Stokes Equations ◽  
First Integral ◽  
Navier Stokes ◽  
Incompressible Fluid Flow ◽  
Navier Stokes Equations ◽  
Particular Solutions

Procedure for constructing exact solutions of 3D Navier–Stokes equations for an incompressible fluid flow is proposed. It is based on the relations representing the previously obtained first integral of the Navier–Stokes equations. A primary generator of particular solutions is proposed. It is used to obtain new classes of exact solutions

A first integral of Navier–Stokes equations and its applications

2010 ◽  
Vol 467 (2125) ◽  
pp. 127-143 ◽  
Author(s):  
Markus Scholle ◽  
André Haas ◽  
Philip H. Gaskell
Keyword(s):  
Stokes Equations ◽  
Scalar Potential ◽  
First Integral ◽  
Inviscid Flow ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Bernoulli’S Equation ◽  
Two Dimensional Flow ◽  
Laminar Shear Flow

Although it is well known that Bernoulli's equation is obtained as the first integral of Euler's equations in the absence of vorticity and that in the case of non-vanishing vorticity a first integral of them can be found using the Clebsch transformation for inviscid flow, generalization of the procedure for viscous flow has remained elusive. Accordingly, in this paper, a first integral of the Navier–Stokes equations for steady flow is constructed. In the case of a two-dimensional flow, this is made possible by formulating the governing equations in terms of complex variables and introducing a new scalar potential. Associated boundary conditions are considered, and an extension of the theory to three dimensions is proposed. The capabilities of the new approach are demonstrated by calculating a Reynolds number correction to the laminar shear flow generated in the narrow gap between a flat moving and a stationary wavy wall, as is often encountered in lubrication problems. It highlights the first integral as a suitable tool for the development of new analytical and numerical methods in fluid dynamics.

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.

Sensitivity analysis for Navier-Stokes equations on unstructured meshes using complex variables

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 56-63
Author(s):  
W. Kyle Anderson ◽  
James C. Newman ◽  
David L. Whitfield ◽  
Eric J. Nielsen
Keyword(s):  
Sensitivity Analysis ◽  
Stokes Equations ◽  
Unstructured Meshes ◽  
Complex Variables ◽  
Navier Stokes ◽  
Navier Stokes Equations

Numerical solution of the reduced Navier-Stokes equations for internal incompressible flows

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1603-1614
Author(s):  
Martin Scholtysik ◽  
Bernhard Mueller ◽  
Torstein K. Fannelop
Keyword(s):  
Numerical Solution ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations
Sign in / Sign up

Export Citation Format

Share Document