Download presentation

Presentation is loading. Please wait.

Published bySarah Winland Modified over 3 years ago

1
Effect of Pressure Gradient on the flow in a Boundary Layer Pressure gradient is found from freestream (external) velocity field Boundary layer equation: x z

2
Effect of Pressure Gradient on the flow in a Boundary Layer In the accelerating part of the stream, At the wall, the boundary layer equation becomes: x z

3
Effect of Pressure Gradient on the flow in a Boundary Layer x z In the decelerating part of the stream, inflection point

4
Effect of Pressure Gradient on the flow in a Boundary Layer x z Velocity distribution suggests that a ∂p/∂x > 0 contributes to thicken the boundary layer, as seen from continuity: Deceleration also adds viscous effects to make the boundary layer grow --- both viscous effects and advection contribute to b.l. growth --- w is directed away from the wall ( ∂u/∂x - ) – increase in b.l. thickness with x

5
Effect of Pressure Gradient on the flow in a Boundary Layer x z ∂p/∂x < 0 pressure gradient is “favorable” ∂p/∂x > 0 pressure gradient is “adverse” or “uphill” Rapid growth of boundary layer and large w field causes “flow separation”

6
from Kundu’s book u = 0 Separation point = boundary between forward flow and backward flow near wall Drag caused by adverse pressure gradient = form drag Boundary layer equations only valid as far as the point of separation

7
Analytical solutions of viscous flows can be found for Re << 1 Negligible inertial forces – Couette & Poiseuille flows

8
Analytical solutions of viscous flows can be found for Re >> 1 Negligible viscous forces, except near a surface -- match irrotational outer (freestream) flow with boundary layer near surface

9
Low ReLow Re << 11×10 3 < Re < 2×10 5 Re > 2×10 5 For intermediate Re, more difficult analytical solutions – experiments and numerical solutions

10
www.soton.ac.uk/ses/outreach/greenpower/boundarylayers.html

11
Another example https://www.arl.psu.edu/ capabilities/fsm.html

12
http://www.iafr.eu/TESI/5.htm#_Toc243930577

13
http://upload.wikimedia.org/wikipedia/commons/b/b4/Vortex-street-animation.gif von Karman Vortex Street

14
Re= 50 Re= 75 Re= 120

15
http://alg.umbc.edu/usaq/archives/001854.html

16
http://www.designyourway.net/blog/inspiration/extraordinary-satellite-photos-of-earth/ Aleutian Islands Application of vortex shedding

Similar presentations

OK

MECH 221 FLUID MECHANICS (Fall 06/07) Chapter 7: INVISCID FLOWS

MECH 221 FLUID MECHANICS (Fall 06/07) Chapter 7: INVISCID FLOWS

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on acid-base indicators you can make at home Ppt on mobile phone based attendance tracking system Ppt on eia report Ppt on new technology in mobiles Viewer ppt online reader Ppt on hydro power station Ppt on computer languages of the 80's Business ppt on flipkart online Ppt on management by objectives steps Ppt on suspension type insulators definition