Fluid Mechanics. Professor Brian Launder Room GB/C031. Flow Management : An introduction

Transcription

1 Fluid Mechanics Professor Brian Launder Room GB/C031 Flow Management : An introduction 1

2 A working definition Flow Management: the modification of the character of a flow to achieve beneficial outcomes. In the present lecture series we interpret this more narrowly to mean devices and strategies which: keep the boundary layer or shear flow laminar when in the absence of flow management it would become turbulent, e.g. laminar flow wing. OR if the boundary layer is already turbulent, strategies which reduce turbulent mixing, usually to reduce the drag OR cause the boundary layer to become turbulent where without flow management, it would remain laminar e.g. trip wires on a cylinder to reduce drag or raise heat transfer. 2

3 Example: Drag on a golf ball It is well known that when the boundary layer becomes turbulent over the leading portion of a sphere, separation occurs later and the drag coefficient is thereby reduced by 75% or more. However, given the dimensions of golf ball, it is not practicable to reach a Reynolds number of for a smooth ball and a human hitter. In the mid-19 th century golfers discovered that worn balls (with nicks and imperfections on their surface) travelled further than new, perfectly smooth ones Drag coefficient for a smooth sphere as a function of Reynolds number 3

4 The effect of dimples As seen from the diagrams the dimpled ball undergoes transition at a lower Reynolds number and this reduces the separation region on the rear of the ball. Experiments suggest that hexagonally shaped golf balls reduce drag even further. 4

5 Types of flow-management device Wall suction Riblets Large-eddy break-up devices (LEBUs) Swirl promoters and streamline curvature devices Polymeric additives Smart surface-perturbation devices Moving surface devices 5

6 Use of wall suction to prevent transition to turbulent flow On a smooth surface, transition point highly sensitive to shape of boundary layer velocity profile. The sign of 2 U/ y 2 at the wall has very great effect on stability of a laminar boundary layer 2 U/ y 2 >0 2 U/ y 2 =0 2 U/ y 2 <0 H δ*/θ From the accompanying stability charts it is evident that a positive pressure gradient (which makes 2 U/ y 2 >0 at wall) greatly reduces Re at which transition will occur. 6

7 The boundary layer equation at a wall For an impermeable wall x-momentum equation at the wall (y=0) reduces to: 0= -dp/dx +µd 2 U/dy 2 Clearly a positive dp/dx makes d 2 U/dy 2 at wall positive, reducing stability and hastening transition. However, if suction is applied at the wall then:. d 2 U/dy 2 w = [dp/dx +ρv w du/dy w ]/µ With suction, V w is negative and by suitably adjusting the rate of fluid withdrawal through the wall the second derivative can be made zero or even negative. Required suction velocity typically 10-3 of the free stream velocity Note that besides altering the boundary layer shape suction reduces the thickness of the boundary layer (and thus the Reynolds number) which also helps to reduce the risk of transition 7

8 Practical considerations Serious attempts to apply laminar flow control by way of suction to wings dates from the 1930s. Early attempts employed sintered materials which are slightly porous. BUT: small pores can get easily clogged; at high speeds the surface does not behave as perfectly smooth; sintered materials have limited strength. For these reasons attention shifted to drilling holes through a solid sheeting. Addition of suction adds significantly to the weight of the aircraft. To achieve a fully laminar wing approximately half the propulsive power goes into the boundary layer suction system J. E. Green AIAA Paper , Research still proceeds (see Green, 2008). 8

9 Autogenous separation control An approach that seeks to avoid the weight penalty and operational complexities of suction control by inserting a porous patch on a surface where separation would otherwise be likely to occur. Seems especially suited for preventing boundary layer separation following a shockwave. See below: 9

10 A question for you In flow over turbine blades there are commonly several rows of holes through which air passes. However, in this case the air is directed from the blade to the external boundary layer (i.e. blowing rather than suction). Why does this not cause boundary-layer separation and what is the purpose of blowing? 10