Day 24: Flow around objects case 1) fluid flowing around a fixed object (e.g. bridge pier) case 2) object travelling within a fluid (cars, ships planes) two forces are exerted between the fluid and the object related to: Skin Friction (Ch9), Drag, Lift (Ch 11) case 1) the flow around it is slowed down while the object experiences a drag force case 2) the object is slowed down while the fluid around it is accelerated
Equivalent Boundary conditions The object moves with velocity u o far away from the object, the fluid velocity is 0 The object is stationary far away from the object, the fluid velocity is u o. Both fluid and object are moving; far away from the object, the relative fluid velocity is u o. Consider the relative free stream velocity = u o. plane flying with or against the wind
Lift / drag When an object is submerged in a flowing fluid, or the object moves in a stationary fluid the fluid is forced to flow around the object. As a result, the object is subjected to forces perpendicular and parallel to free stream velocity Drag: forces parallel to free stream velocity Lift: forces perpendicular to free stream velocity
The resultant force exerted by the fluid on the object has two components : parallel to the incoming velocity DRAG perpendicular to the incoming velocity LIFT
Consider drag on a cylinder for different free stream velocities: Increasing free stream velocities and Reynolds number To model the forces, we start by focusing on simple systems Drag on a surface alone can be complicated, velocity dependent
Drag on a surface 2 types Pressure stress/ distribution > form drag Shear stress > skin friction drag
Total drag force component parallel to the relative (free stream) velocity induced by the fluid on an object = pressure drag + skin friction For precise design, we need to consider pressure and skin friction at each point and sum these for total drag. Integral along the chord length profile F D chord p cos da sin da chord form drag friction drag
Shortcuts for total drag For less precise design and/or well-known / well-studied (simple) objects, we rely on dimensional analysis and experimental studies for an average coefficient of drag FD 2 FD CD V A 2 V A 2 CD 2 Here, A is a reference area, sometimes frontal area NO from tables if Re independent YES
2D BODY (sectional drag coeff.) L / D>20 : 2D assumptions note that even if C d goes down F d still increases (prop. to V 2 )!! CD is Reynolds independent when flow separation (thus form drag) is dominant
Shortcuts for total drag FD V A CD 2 2 For less precise design and/or well-known / wellstudied (simple) objects, we rely on charts for an average coefficient of drag F D C D V A E.g., cylinders & spheres 2 2
flow separation controls the wake region characterized by low pressure a change of regime (laminar > turbulent) in the boundary layer of the cylinder retard the separation : the flow in the wake is more mixed, the pressure is not as low, as the velocity increases as the upwind downwind pressure decreases, Cd decreases considerably lam > turb transition
can we control drag by controlling lam > turb transition? Yes with surface roughness! as the surface roughness increases the transition occurs earlier (lower Re ) At this RE the smaller Cd is obtained for a rough surface
Other ways to reduce drag? reduce form drag (streamlining) reduce frictional drag (materials) delay transition (stay in laminar regime) use roughness in a small range of Reynolds numbers (e.g. for UAV) use surfactants, polymers to change the apparent flow viscosity at the wall (water) use super-hydrophobic surface (water)
https://www.youtube.com/watch?v=sv_6e 1Lh7yo https://www.youtube.com/watch?v=cde7i T-EsZ0
Drag on a sphere (important to calculate the terminal velocity of droplets in air or sediments in water) F D 3 π μ V0 d Stokes drag in the laminar regime for Re<1 for settling velocity, impose Buoyancy +F D = Weight and obtain V S but we also have F D C D V 2 A 2 Both equations are satisfied when C D = 24/Re normalized drag decreases with the Reynolds number (providing the flow stays laminar, same story of the pipe flow) for larger spheres or faster flows, Re increases as well as Cd (with respect to the laminar case) C D 24 0. 687 (1 0.15 Re Re ) lam regine > turbulent
vortex shedding vortex shedding is a drag related phenomena, induced by an instability in a shear layer a flow region with high velocity gradient 1) 2)
http://www.youtube.com/watch?v=3mclp9qmcgs shear layer shear layer shedded vortices with predictable periodicity layer St = n D/ V 0 n is the shedding frequency = 1/ Time between vortices
Lift next week...