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

ES 202 Fluid & Thermal Systems 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 Lecture 27 ES 202 Fluid & Thermal Systems

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 Lecture 27 ES 202 Fluid & Thermal Systems

ES 202 Fluid & Thermal Systems “Snow-Rollers” (taken from www.wtwo.com) Lecture 27 ES 202 Fluid & Thermal Systems

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 Lecture 27 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. Lecture 27 ES 202 Fluid & Thermal Systems

Motivation: The Commercial Side Drag optimization on airplanes and automobiles Design for turbomachinery (compressor and turbine) lower surface upper surface Pressure coefficient at Mach 2.2 Blade design in turbomachinery using computational methods Images taken from Aerospace Computing Laboratory, Stanford University Lecture 27 ES 202 Fluid & Thermal Systems

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 Lecture 27 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. Lecture 27 ES 202 Fluid & Thermal Systems

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. Lecture 27 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: Lecture 27 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 strongly Reynolds number dependent and geometry dependent (slender versus blunt bodies). Lecture 27 ES 202 Fluid & Thermal Systems

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 Lecture 27 ES 202 Fluid & Thermal Systems

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. Lecture 27 ES 202 Fluid & Thermal Systems

Pressure Coefficient over a Cylinder Taken from Figure 3.49 in “Fundamentals of Aerodynamics” by John D. Anderson Jr. q subcritical supercritical inviscid q, degrees Lecture 27 ES 202 Fluid & Thermal Systems

Example on Drag Coefficient of a cylinder in cross-flow Lecture 27 ES 202 Fluid & Thermal Systems