**ES 202Fluid and Thermal SystemsLecture 27:Drag on Cylinders** and Spheres(2/13/2003)

**Assignments** • Homework: • 13-12C, 13-13C, 13-33, 13-40E • add the phrase “at high Reynolds numbers” to 13-13C • only hand in Tuesday homework next Monday • Reading: • 13-7 to 13-8 ES 202 Fluid & Thermal Systems

**Announcements** • Problem session this evening at 7 pm • hydrostatics • Exam 2 solutions • external flows • Due date for Lab 3 write-up • Undergraduate Research Awards • Fluid mechanics made it to the news • “snow-rollers” on the ground ES 202 Fluid & Thermal Systems

**“Snow-Rollers”** (taken from www.wtwo.com) ES 202 Fluid & Thermal Systems

**Road Map of Lecture 27** Knowledge items: • Drag on flat plates • finish up control volume analysis of drag on a flat plate • definition of friction coefficient for flat plates • Drag on cylinders • categorization of drag components • Reynolds number dependency of drag • artifact of viscosity: flow separation • drag coefficients for cylinders • laminar versus turbulent boundary layers • Drag on spheres • effects of a trip wire, dimples on a golf ball Examples: • Dimensional analysis of skin friction over flat plate • Drag on a cylinder due to a cross-flow in open air ES 202 Fluid & Thermal Systems

**Motivation: The Fun Side** • Dimples on golf ball • Any cyclist here? • concept of drafting in bike racing, formula 1 racing • the V-shaped pattern in bird migration • Design of aerodynamic helmet • Design of sail and yacht • Outfit on world record holding cyclists, swimmers, runners, etc. ES 202 Fluid & Thermal Systems

**upper surface** lower surface Pressure coefficient at Mach 2.2 Blade design in turbomachinery using computational methods Motivation: The Commercial Side • Drag optimization on airplanes and automobiles • Design for turbomachinery (compressor and turbine) Images taken from Aerospace Computing Laboratory, Stanford University ES 202 Fluid & Thermal Systems

**Quiz on Lecture 26** • What does the boundary layer thickness at a particular streamwise location on a flat plate depend on? • At the same streamwise location, what is the qualitative change in the boundary layer thickness if: • the free-stream air speed doubles • air is replaced by a less viscous fluid • Again at the same streamwise location, what do you expect the boundary layer thickness to behave if the flow speed is doubled? • double/less than double/more than double • half/less than half/more than half • no change ES 202 Fluid & Thermal Systems

**Comparison of Fluid Properties** At the same flow speed and object size, the Reynolds number in water is 10 times larger than that in air. This information is useful in interpreting the difference in flow patterns between air and water. ES 202 Fluid & Thermal Systems

**Drag on a Flat Plate** • Due to viscous (fluid friction) effects, the flat plate will experience a force in the downstream direction. The force is termed “Drag”. • Think of it as an action-reaction pair of force: • the fluid experiences a force in the upstream direction to slow it down; • the same force (in magnitude) acts on the flat plate in opposite direction. • Exercise: Perform a control volume analysis on a flat plate to find out its total drag • choice of top boundary • concept of momentum deficit • Suggest another way to find the drag on a flat plate. ES 202 Fluid & Thermal Systems

**Friction Coefficient on a Flat Plate** • As the boundary layer thickens in the streamwise direction, what do you expect the local friction drag to behave? • Exercise: Perform a dimensional analysis on the total drag force on a flat plate of length L and width w. • Definition of friction coefficient: ES 202 Fluid & Thermal Systems

**Categorization of Drag Components** • The total drag force on an object can be broadly classified into two categories: Total drag force • Friction drag • directly related to • skin friction on surfaces • Pressure (form) drag • indirectly related to fluid viscosity • due to momentum losses through viscosity • mostly involves flow separation • Relative importance between friction drag and pressure drag is stronglyReynolds number dependent and geometry dependent (slender versus blunt bodies). ES 202 Fluid & Thermal Systems

**Pressure Drag** • The flat plate boundary layer illustrates the origin of friction drag which is directly related to the viscosity of a fluid and the no-slip boundary condition at a solid surface. • Another drag component which is indirectly related to the viscosity of a fluid is called the pressure drag, which is absent in the flat plate case. • Pressure drag is due to the difference in pressure forces between the front and back side of an object. • The difference in pressure distribution is indirectly related to viscous effects (phenomena of flow separation). • Definition of pressure coefficient over a cylinder ES 202 Fluid & Thermal Systems

**Flow Separation** • Flow separation is an artifact of fluid friction • think of blowing versus suction (application to pipe inlet and outlet) • Show visualizations from MMFM: • Boundary layer transition • Conditions producing separation • Pressure losses and drag • Effects of boundary conditions on separation • Flow over cylinders: effect of Reynolds number • Flow over edges and blunt bodies • Mechanism: The flow does not have enough momentum in the boundary layer to negotiate the pressure hill it has to climb to remain attached. ES 202 Fluid & Thermal Systems

**q** Pressure Coefficient over a Cylinder Taken from Figure 3.49 in “Fundamentals of Aerodynamics” by John D. Anderson Jr. subcritical supercritical inviscid q, degrees ES 202 Fluid & Thermal Systems

**Example on Drag Coefficient of a cylinder ** in cross-flow ES 202 Fluid & Thermal Systems