scholarly journals Solution of Parapolic Navier-Stokes Equations for Laminar Forced Convective Flow in Entrance Region of a Flat Passage.(Dept.M)

2021 ◽  
Vol 16 (2) ◽  
pp. 60-70
Author(s):  
Mohamed Wasel
Keyword(s):  
Convective Flow ◽  
Stokes Equations ◽  
Entrance Region ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Forced Convective Flow

scholarly journals NUMERICAL CALCULATION OF CONVECTIVE FLOW OF GAS AT CIRCULAR-TYPE SCHEME OF HEATING

2015 ◽  
pp. 87-93
Author(s):  
E. M. Sorokina ◽  
A. G. Obukhov
Keyword(s):  
Convective Flow ◽  
Stokes Equations ◽  
Complete System ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Boundary Condi Tions ◽  
Navier Stokes Equations ◽  
Viscous Heat ◽  
Condi Tions

To investigate the convective flows of polytropic gas a complete system of Navier - Stokes equations is consid-ered. As the initial and boundary conditions the specific ratios are offered. The proposed initial and boundary condi-tions realization is carried out at construction of the numerical solution of the complete system of Navier - Stokes equations for modeling the unsteady state three-dimensional convection flows of the compressible viscous heat-conducting gas in the isolated cubic area. Three components of the velocity vector are calculated for the initial stage of the convective flow. It is shown that the velocity components are complex and depend essentially on the heating shape, height and time.

A Contribution to the Numerical Solution of Developing Laminar Flow in the Entrance Region of Concentric Annuli With Rotating Inner Walls

1974 ◽  
Vol 96 (4) ◽  
pp. 333-340 ◽  
Author(s):  
J. E. R. Coney ◽  
M. A. I. El-Shaarawi
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Stokes Equations ◽  
Complete Solution ◽  
Numerical Differentiation ◽  
Velocity Profiles ◽  
Entrance Region ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Special Case

The boundary layer simplification of the Navier-Stokes equations for hydrodynamically developing laminar flow with constant physical properties in the entrance region of concentric annuli with rotating inner walls have been numerically solved using a simple linearized finite-difference scheme. Additional results to those existing in the literature by Martin and Payne [1–2] will be presented here. An advantage of the analysis used in this paper is that it does not solve for the stream function and vorticity, but predicts the development of tangential, axial and radial velocity profiles directly, thus avoiding numerical differentiation. Results for the development of these velocity profiles, pressure drop and friction factor are presented for five annuli radii ratios (0.3, 0.5, 0.674, 0.727 and 0.90) at various values of the parameter Re2/Ta. The paper may be considered as a direct comparison between the boundary layer solution and the complete solution of the Navier-Stokes equations [1–2] for that special case.

Laminar flow in the entrance region of a smooth pipe

1979 ◽  
Vol 90 (3) ◽  
pp. 433-447 ◽  
Author(s):  
A. K. Mohanty ◽  
S. B. L. Asthana
Keyword(s):  
Boundary Layers ◽  
Stokes Equations ◽  
Velocity Profiles ◽  
Entrance Region ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fourth Degree ◽  
Boundary Layer Equations ◽  
Inlet Region ◽  
Order Of Magnitude

The entrance region has been divided into two parts, the inlet region and the filled region. At the end of the inlet region, the boundary layers meet at the pipe axis but the velocity profiles are not yet similar. In the filled region, adjustment of the completely viscous profile takes place until the Poiseuille similar profile is attained at the end of it. The boundary-layer equations in the inlet region and the Navier-Stokes equations with order-of-magnitude analysis in the filled region are solved using fourth-degree velocity profiles. The total length of the entrance region so obtained is ξ = x/R Re = 0·150, whereas the boundary layers are observed to meet at approximately one-quarter of the entrance length, i.e. at ξ = 0·036. Experiments reported in the paper corroborate the analytical results.

Laminar Incompressible Flow in the Entrance Region of Ducts of Arbitrary Cross Section

1971 ◽  
Vol 93 (1) ◽  
pp. 113-117 ◽  
Author(s):  
James A. Miller
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Arbitrary Cross Section ◽  
Entrance Region ◽  
Navier Stokes ◽  
Initial Value ◽  
Navier Stokes Equations ◽  
Friction Factors

A combination of the numerical technique of Chorin for the solution of the Navier-Stokes equations and a transformation of the initial value problem to a boundary value problem is shown to allow calculation of the laminar hydrodynamic entrance region of ducts of arbitrary cross section. Numerical examples consisting of the solution for ducts of square and triangular cross sections are presented along with the associated friction factors.

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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