Uniform Flow and a Region near The Stagnation Point: The Vorticity Equation and its Balance
Journal Title: International Journal of Innovation in Science and Mathematics - Year 2018, Vol 6, Issue 3
Abstract
A local description for the uniform flow past the leading surface of a bluff body such as a cylinder is to consider the region near the stagnation point. The body surface is assumed to be flat, locally and corresponds to the boundary at y = 0 with the stagnation point at x = 0, y = 0. If the flow is inviscid, the flow is locally given by the u = alpha times x and v = - alpha times y, for alpha > 0. The corresponding stream function is psi = alpha * x*y. We show that this satisfies the inviscid flow boundary conditions at the surface but not the viscous conditions. We formulate the vorticity equation using the stream function and show that a solution can be found with psi = alpha * x *f(y/delta) for some function f of eta that satisfies the viscous conditions and matches the inviscid flow far above the surface. We determine the length scale delta and derive the nonlinear differential equation for f of eta and find the vorticity balance in this flow.
Authors and Affiliations
Steve Anglin
Keywords
Related Articles
- EP ID EP498538
- DOI -
- Views 80
- Downloads 0
Reduced Euler Equations in Turbulent Incompressible Flows where Pressure Has Isotropy Assumption
We look at reduced Euler Equations in turbulent incompressible flows where pressure has isotropy assumption where we find that vorticity is relative to principle axes. We solve and find how vorticity gives an energy spec...
Alternative to Reduced Euler Equations in Turbulent Incompressible Flows where Pressure Has Isotropy Assumption: Vorticity Spectrum
We look at reduced Euler Equations in turbulent incompressible flows where pressure has isotropy assumption where we find that vorticity is relative to principle axes. We solve and find how vorticity gives an en...
Development of Pre-service Teacher Activity Sheets with Concrete-Representational-Abstract (Cra) Approach for Mathematical Logical thinking Ability
The purpose of this research is to produce pre-service teacher activity sheets with Concrete-Representational-Abstract (CRA) approachinkapita selekta because pre-service teacher activity sheets not available based...
Uniform Flow and a Region near The Stagnation Point: The Vorticity Equation and its Balance
A local description for the uniform flow past the leading surface of a bluff body such as a cylinder is to consider the region near the stagnation point. The body surface is assumed to be flat, locally and corresponds to...
Improving Heat Transfer through Paraffin Wax for Sustainability Heat Pump
The objective of the present work is to study the effect of the solar collector inclination angle, paraffin specifications and paraffine cavity high on the performance of the thermal pump numerically at different time. A...