Basic Aerodynamics - Aerospace Practicum - Lecture Slides, Slides of Aerospace Engineering

Download Basic Aerodynamics - Aerospace Practicum - Lecture Slides and more Slides Aerospace Engineering in PDF only on Docsity! 1 AEROSPACE PRACTICUM Lecture 3: Introduction to Basic Aerodynamics 2 Docsity.com 2 READING AND HOMEWORK ASSIGNMENTS • Reading: Introduction to Flight, by John D. Anderson, Jr. – For this week’s lecture: Chapter 4, Sections 4.1 - 4.9 – For next week’s lecture: Chapter 4, Sections 4.10 - 4.21, 4.27 • Lecture-Based Homework Assignment: – Problems: 4.1, 4.2, 4.4, 4.5, 4.6, 4.8, 4.11, 4.15, 4.16 • DUE: Friday, February 8, 2013 by 11:00 am • Turn in hard copy of homework – Also be sure to review and be familiar with textbook examples in Chapter 4 • Lab this week: – Machine shop (remember to dress appropriately, no ‘open-toe’ shoes) – Team Challenge #1 Docsity.com 5 SUMMARY OF GOVERNING EQUATIONS (4.8) STEADY AND INVISCID FLOW 2 22 2 11 2211 2 1 2 1 VpVp VAVA ρρ +=+ = ( ) 222 111 2 22 2 11 1 2 1 2 1 2 1 222111 2 1 2 1 RTp RTp VTcVTc T T p p VAVA pp ρ ρ ρ ρ ρρ γ γγ = = +=+       =      = = − • Incompressible flow of fluid along a streamline or in a stream tube of varying area • Most important variables: p and V • T and ρ are constants throughout flow • Compressible, isentropic (adiabatic and frictionless) flow along a streamline or in a stream tube of varying area • T, p, ρ, and V are all variables continuity Bernoulli continuity isentropic energy equation of state at any point Docsity.com CONSERVATION OF MASS (4.1) • Physical Principle: Mass can be neither created nor destroyed Stream tube • As long as flow is steady, mass that flows through cross section at point 1 (at entrance) must be same as mass that flows through point 2 (at exit) • Flow cannot enter or leave any other way (definition of a stream tube) • Also applies to solid surfaces, pipe, funnel, wind tunnels, airplane engine • “What goes in one side must come out the other side” A1 A2 V1 V2 Funnel wall Docsity.com CONSERVATION OF MASS (4.1) Stream tube • Consider all fluid elements in plane A1 • During time dt, elements have moved V1dt and swept out volume A1V1dt • Mass of fluid swept through A1 during dt: dm=ρ1(A1V1dt) A1: cross-sectional area of stream tube at 1 V1: flow velocity normal (perpendicular) to A1 21 2222 1111 s kg Flow Mass mm VAm VAm dt dm    = =      === ρ ρ Docsity.com 10 APPLYING NEWTON’S SECOND LAW FOR FLOWS dx dz dy x y z Consider a small fluid element moving along a streamline Element is moving in x-direction V What forces act on this element? 1. Pressure (force x area) acting in normal direction on all six faces 2. Frictional shear acting tangentially on all six faces (neglect for now) 3. Gravity acting on all mass inside element (neglect for now) Note on pressure: Always acts inward and varies from point to point in a flow Docsity.com 11 APPLYING NEWTON’S SECOND LAW FOR FLOWS dx dz dy p (N/m2) Area of left face: dydz Force on left face: p(dydz) Note that P(dydz) = N/m2(m2)=N Forces is in positive x-direction x y z Docsity.com 12 APPLYING NEWTON’S SECOND LAW FOR FLOWS dx dz dy p (N/m2) Area of left face: dydz Force on left face: p(dydz) Forces is in positive x-direction p+(dp/dx)dx (N/m2) Change in pressure per length: dp/dx Change in pressure along dx is (dp/dx)dx Force on right face: [p+(dp/dx)dx](dydz) Forces acts in negative x-direction x y z Pressure varies from point to point in a flow There is a change in pressure per unit length, dp/dx Docsity.com 15 SUMMARY: EULER’S EQUATION ( ) ( ) VdVdp dx dVVdxdydzdxdydz dx dp maF ρ ρ −= =− = Euler’s Equation • Euler’s Equation (Differential Equation) – Relates changes in momentum to changes in force (momentum equation) – Relates a change in pressure (dp) to a chance in velocity (dV) • Assumptions we made: – Neglected friction (inviscid flow) – Neglected gravity – Assumed that flow is steady Docsity.com 16 WHAT DOES EULER’S EQUATION TELL US? • Notice that dp and dV are of opposite sign: dp = -ρVdV • IF dp ↑ – Increased pressure on right side of element relative to left side – dV ↓ Docsity.com 17 WHAT DOES EULER’S EQUATION TELL US? • Notice that dp and dV are of opposite sign: dp = -ρVdV • IF dp ↑ – Increased pressure on right side of element relative to left side – dV ↓ (flow slows down) • IF dp ↓ – Decreased pressure on right side of element relative to left side – dV ↑ (flow speeds up) • Euler’s Equation is true for Incompressible and Compressible flows Docsity.com 20 WHEN AND WHEN NOT TO APPLY BERNOULLI YES NO Docsity.com 21 SIMPLE EXAMPLE p1 = 1.2x105 N/m2 T1 = 330 K V1 = 10 m/s A1 = 5 m2 p2 = ? T2 = 330 K V2 = 30 m/s A2 = 1.67 m2 Since flow speed < 100 m/s assume flow is incompressible (ρ1=ρ2) Given air flow through converging nozzle, what is exit pressure, p2? ( )( ) ( ) ( )( ) 25225222112 3 5 1 1 1 10195.1301027.1 2 1102.1 2 1 27.1 330287 102.1 m NxxVVpp m kgx RT p =−+=−+= === ρ ρ Since velocity is increasing along flow, it is an accelerating flow Notice that even with a 3-fold increase in velocity pressure decreases by only about 0.8 %, which is characteristic of low velocity flow Docsity.com HOW DOES AN AIRFOIL GENERATE LIFT? • Lift due to imbalance of pressure distribution over top and bottom surfaces of airfoil (or wing) – If pressure on top is lower than pressure on bottom surface, lift is generated – Why is pressure lower on top surface? • We can understand answer from basic physics: – Continuity (Mass Conservation) – Newton’s 2nd law (Euler or Bernoulli Equation) Lift = PA Docsity.com