Chapter 11 Flow over bodies Lift and Drag

Chapter 11: Flow over bodies; Lift and Drag Eric G. Paterson Department of Mechanical and Nuclear Engineering The Pennsylvania State University Spring 2005

Note to Instructors These slides were developed 1, during the spring semester 2005, as a teaching aid for the undergraduate Fluid Mechanics course (ME 33: Fluid Flow) in the Department of Mechanical and Nuclear Engineering at Penn State University. This course had two sections, one taught by myself and one taught by Prof. John Cimbala. While we gave common homework and exams, we independently developed lecture notes. This was also the first semester that Fluid Mechanics: Fundamentals and Applications was used at PSU. My section had 93 students and was held in a classroom with a computer, projector, and blackboard. While slides have been developed for each chapter of Fluid Mechanics: Fundamentals and Applications, I used a combination of blackboard and electronic presentation. In the student evaluations of my course, there were both positive and negative comments on the use of electronic presentation. Therefore, these slides should only be integrated into your lectures with careful consideration of your teaching style and course objectives. Eric Paterson Penn State, University Park August 2005 1 These slides were originally prepared using the La. Te. X typesetting system (http: //www. tug. org/) and the beamer class (http: //latex-beamer. sourceforge. net/), but were translated to Power. Point for wider dissemination by Mc. Graw-Hill. ME 33 : Fluid Flow 2 Chapter 11: Flow over bodies; lift and drag

Objectives Have an intuitive understanding of the various physical phenomena such as drag, friction and pressure drag, drag reduction, and lift. Calculate the drag force associated with flow over common geometries. Understand the effects of flow regime on the drag coefficients associated with flow over cylinders and spheres Understand the fundamentals of flow over airfoils, and calculate the drag and lift forces acting on airfoils. ME 33 : Fluid Flow 3 Chapter 11: Flow over bodies; lift and drag

Motivation ME 33 : Fluid Flow 4 Chapter 11: Flow over bodies; lift and drag

Motivation ME 33 : Fluid Flow 5 Chapter 11: Flow over bodies; lift and drag

External Flow Bodies and vehicles in motion, or with flow over them, experience fluid-dynamic forces and moments. Examples include: aircraft, automobiles, buildings, ships, submarines, turbomachines. These problems are often classified as External Flows. Fuel economy, speed, acceleration, maneuverability, stability, and control are directly related to the aerodynamic/hydrodynamic forces and moments. General 6 DOF motion of vehicles is described by 6 equations for the linear (surge, heave, sway) and angular (roll, pitch, yaw) momentum. ME 33 : Fluid Flow 6 Chapter 11: Flow over bodies; lift and drag

Fluid Dynamic Forces and Moments Ships in waves present one of the most difficult 6 DOF problems. ME 33 : Fluid Flow 7 Airplane in level steady flight: drag = thrust and lift = weight. Chapter 11: Flow over bodies; lift and drag

Drag and Lift Fluid dynamic forces are due to pressure and viscous forces acting on the body surface. Drag: component parallel to flow direction. Lift: component normal to flow direction. ME 33 : Fluid Flow 8 Chapter 11: Flow over bodies; lift and drag

Drag and Lift and drag forces can be found by integrating pressure and wall-shear stress. ME 33 : Fluid Flow 9 Chapter 11: Flow over bodies; lift and drag

Drag and Lift In addition to geometry, lift FL and drag FD forces are a function of density and velocity V. Dimensional analysis gives 2 dimensionless parameters: lift and drag coefficients. Area A can be frontal area (drag applications), planform area (wing aerodynamics), or wettedsurface area (ship hydrodynamics). ME 33 : Fluid Flow 10 Chapter 11: Flow over bodies; lift and drag

Drag and Lift For applications such as tapered wings, CL and CD may be a function of span location. For these applications, a local CL, x and CD, x are introduced and the total lift and drag is determined by integration over the span L ME 33 : Fluid Flow 12 Chapter 11: Flow over bodies; lift and drag

Friction and Pressure Drag Friction drag Fluid dynamic forces are comprised of pressure and friction effects. Often useful to decompose, FD = FD, friction + FD, pressure CD = CD, friction + CD, pressure Pressure drag This forms the basis of ship model testing where it is assumed that CD, pressure = f(Fr) CD, friction = f(Re) Friction & pressure drag ME 33 : Fluid Flow 14 Chapter 11: Flow over bodies; lift and drag

Streamlining reduces drag by reducing FD, pressure, at the cost of increasing wetted surface area and FD, friction. Goal is to eliminate flow separation and minimize total drag FD Also improves structural acoustics since separation and vortex shedding can excite structural modes. ME 33 : Fluid Flow 15 Chapter 11: Flow over bodies; lift and drag

Streamlining ME 33 : Fluid Flow 16 Chapter 11: Flow over bodies; lift and drag

CD of Common Geometries For many geometries, total drag CD is constant for Re > 104 CD can be very dependent upon orientation of body. As a crude approximation, superposition can be used to add CD from various components of a system to obtain overall drag. However, there is no mathematical reason (e. g. , linear PDE's) for the success of doing this. ME 33 : Fluid Flow 18 Chapter 11: Flow over bodies; lift and drag

CD of Common Geometries ME 33 : Fluid Flow 19 Chapter 11: Flow over bodies; lift and drag

CD of Common Geometries ME 33 : Fluid Flow 20 Chapter 11: Flow over bodies; lift and drag

CD of Common Geometries ME 33 : Fluid Flow 21 Chapter 11: Flow over bodies; lift and drag

Flat Plate Drag on flat plate is solely due to friction created by laminar, transitional, and turbulent boundary layers. ME 33 : Fluid Flow 22 Chapter 11: Flow over bodies; lift and drag

Flat Plate Drag Local friction coefficient Laminar: Turbulent: Average friction coefficient Laminar: Turbulent: For some cases, plate is long enough for turbulent flow, but not long enough to neglect laminar portion ME 33 : Fluid Flow 23 Chapter 11: Flow over bodies; lift and drag

Effect of Roughness Similar to Moody Chart for pipe flow Laminar flow unaffected by roughness Turbulent flow significantly affected: Cf can increase by 7 x for a given Re ME 33 : Fluid Flow 24 Chapter 11: Flow over bodies; lift and drag

Cylinder and Sphere Drag ME 33 : Fluid Flow 25 Chapter 11: Flow over bodies; lift and drag

Cylinder and Sphere Drag Flow is strong function of Re. Wake narrows for turbulent flow since TBL (turbulent boundary layer) is more resistant to separation due to adverse pressure gradient. sep, lam ≈ 80º sep, lam ≈ 140º ME 33 : Fluid Flow 26 Chapter 11: Flow over bodies; lift and drag

Effect of Surface Roughness ME 33 : Fluid Flow 27 Chapter 11: Flow over bodies; lift and drag

Lift is the net force (due to pressure and viscous forces) perpendicular to flow direction. Lift coefficient A=bc is the planform area ME 33 : Fluid Flow 28 Chapter 11: Flow over bodies; lift and drag

Computing Lift Potential-flow approximation gives accurate CL for angles of attack below stall: boundary layer can be neglected. Thin-foil theory: superposition of uniform stream and vortices on mean camber line. Java-applet panel codes available online: http: //www. aa. nps. navy. mil/~jones/online _tools/panel 2/ Kutta condition required at trailing edge: fixes stagnation pt at TE. ME 33 : Fluid Flow 29 Chapter 11: Flow over bodies; lift and drag

Effect of Angle of Attack Thin-foil theory shows that CL≈2 for < stall Therefore, lift increases linearly with Objective for most applications is to achieve maximum CL/CD ratio. CD determined from windtunnel or CFD (BLE or NSE). CL/CD increases (up to order 100) until stall. ME 33 : Fluid Flow 30 Chapter 11: Flow over bodies; lift and drag

Lift Generated by Spinning Superposition of Uniform stream + Doublet + Vortex ME 33 : Fluid Flow 35 Chapter 11: Flow over bodies; lift and drag

Lift Generated by Spinning CL strongly depends on rate of rotation. The effect of rate of rotation on CD is small. Baseball, golf, soccer, tennis players utilize spin. Lift generated by rotation is called The Magnus Effect. ME 33 : Fluid Flow 36 Chapter 11: Flow over bodies; lift and drag