7 Viscous Effects EAS 4101 S11

7 Viscous Effects EAS 4101 S11 - EAS 4101, S11 University...

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EAS 4101, S11 University of Florida 3/14/11 1/25 Section 7, Viscous Effects 7 Viscous Effects 7.1 Introduction To date, we have focused on I3 flow that possess negligible compressibility, rotationality, and viscous effects. o Incompressible : compressibility effects in the flow are negligible with respect to other effects 00 D V Dt    o Irrotational: there is negligible rotation of the fluid particles, 0 V  . o Inviscid: viscous forces are negligible compared to other forces b DV pf Dt      inviscid b p f Dt   which is Euler’s Equation. For the remainder of the class, we will discuss the effects of viscosity and compressibility , both of which lead to rotationality and drag. 7.1.1 Qualitative Effects of Viscosity Viscous Drag / Skin Friction : The no-slip boundary condition results in wall shear stress that produces a “skin friction” drag force and associated skin friction coefficient, w f C q , where 0 w n u n  for a Newtonian fluid. Separation : The wall shear stress coupled with adverse pressure gradients results in flow separation that produces a pressure drag loss and reduces lift.
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EAS 4101, S11 University of Florida 3/14/11 2/25 Section 7, Viscous Effects Unsteadiness : The no slip boundary condition results in rotationality and velocity gradients, which are required for flow instabilities. These instabilities come in various forms, boundary layers are usually first unstable before transitioning to turbulences and at high angles of attack the separated flow can become an unstable, oscillatory wake. http://www2.icfd.co.jp/menu1/boundarylayerseparation/boundlays.html Turbulence : At a sufficiently high Re x , the flow will transition from the laminar state to turbulent flow. The skin friction and aeroheating will dramatically increase in turbulent flows due to the macroscopic (turbulent) mixing.
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EAS 4101, S11 University of Florida 3/14/11 3/25 Section 7, Viscous Effects 7.1.2 High-Re Number flows Effects of viscosity are confined to narrow region near vorticity generating surfaces. Tracking viscous effects can be done via vorticity, for example consider a 2D, fully developed flow, o convection of vorticity Re ~ diffusion of vorticity UL , where yx z  High-speed fluid sweeps vorticity downstream (convection) before the viscous effects can diffuse vorticity outward from the wall. Boundary Layer: region of flow where viscous effects are important Consider the following two cases possessing identical plate lengths, L , but different Reynolds numbers. Why must we account for viscous effects when the inertial terms dominate in high Re flow?
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This note was uploaded on 09/05/2011 for the course EAS 4101 taught by Professor Sheplak during the Spring '08 term at University of Florida.

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7 Viscous Effects EAS 4101 S11 - EAS 4101, S11 University...

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