Flow types

Internal External• Relative velocity between fluid & object• Auto moving through air• Water moving against bridge abutment• Wind against building

Drag force

Resistance to “forward” motion – push back in direction of fluid flow

Depends on• Fluid/object velocities• Fluid properties• Geometry of object• Surface roughness

Drag Forces

Two types• Friction drag: viscous shear effects as flow

moves over object surface. Acts parallel to surface

• Form drag: affected by geometry of object.

Acts perpendicular to object

Drag force

Theory: integrate pressure & shear forces over object surface.

• Complex mathematics• Empirical approach

Similitude

Model simulates prototype Reliance on dimensionless parameters• Reynolds Number• Relative roughness• Drag coefficient - CD

Wind tunnels

Experimental drag determinations

• Buildings• Ships• Bridge supports/abutments• Vehicles

Wind Tunnel

DC 3 & B 17: about 100 hours of testing F 15: 20 000 hours of testing

Drag Coefficient

FD = CD A ρ (V2/2) V – free stream velocity Characteristic area –e.g. frontal for auto Air density CD – drag coefficient characteristic of

geometry

Drag Coefficient

Includes both pressure & friction drags: one usually dominates

• Airfoil – friction; viscous shear drag• Auto – pressure; form drag

Drag force

Assume for experimentation• No adjacent surfaces• Free stream velocity uniform & steady• No free surface in fluid

Drag force

Simplification: power to move vehicle on level ground

• Rolling friction• Drag force

Vehicles

Early autos – high CD; no concern < 30mph Higher speeds concerns increased Advances in metal-forming techniques for

improved body designs Control CD

• Fuel costs• Conserve non-renewable resources• Pollution

Vehicles

Nose of auto Trunk of auto Surface finish Discontinuities• Mirrors• Door handles• Wheel wells• Air intakes

Vehicles

Reduced drag vs other factors• Visibility• Passenger accommodation• Aesthetics

Fluid Mechanics Lab

Simple shapes• Disk• Hemisphere• Sphere• Teardrop

Pressure drag

Flat disk• All pressure; no friction drag• Streamline separation → wake; low

pressure region. Adverse pressure gradient

P front-to-back

Pressure drag

Sphere• Streamline separation• Wake

Pressure drag

Tear drop – streamline• Reduce separation – farther along surface

yields smaller wake• Increase in friction drag; optimum

streamline design

Shape and flow Formdrag

Skinfriction

            0% 100%

            ~10% ~90%

           ~90% ~10%

           100% 0

Design Process: EWT Models

Photo’s of autos SolidWorks design CFD analysis of design: streamlines, CD

prediction 3D printer for models using SolidWorks design Preparation of models for EWT: surface &

mounting EWT testing: Lab CD vs predicted CD. Agreement

within 10%.