MAE 1202: AEROSPACE PRACTICUM

1. MAE 1202: AEROSPACE PRACTICUM Lecture 6: Compressible and Isentropic Flow 2 Introduction to Airfoils February 25, 2013 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

2. READING AND HOMEWORK ASSIGNMENTS • Reading: Introduction to Flight, by John D. Anderson, Jr. • For this week’s lecture: Chapter 5, Sections 5.1 - 5.5 • Mid-Term Exam: Monday, March 18, 2013 • Exam will be given during laboratory session • Lecture material only (no MATLAB, CAD, etc.) • Covers Chapter 4 and 5 (through 5.5) • Mid-Term Exam Review: week after spring break during evening • Lecture-Based Homework Assignment: • Problems: 5.2, 5.3, 5.4, 5.6 • DUE: Friday, March 1, 2013 by 5 PM • Turn in hard copy of homework • Also be sure to review and be familiar with textbook examples in Chapter 5

3. ANSWERS TO LECTURE HOMEWORK • 5.2: L = 23.9 lb, D = 0.25 lb, Mc/4 = -2.68 lb ft • Note 1: Two sets of lift and moment coefficient data are given for the NACA 1412 airfoil, with and without flap deflection. Make sure to read axis and legend properly, and use only flap retracted data. • Note 2: The scale for cm,c/4 is different than that for cl, so be careful when reading the data • 5.3: L = 308 N, D = 2.77 N, Mc/4 = - 0.925 N m • 5.4:a = 2° • 5.6: (L/D)max ~ 112

4. e (J/kg) 1st LAW OF THERMODYNAMICS (4.5) Boundary SYSTEM (unit mass of gas) SURROUNDINGS dq • System (gas) composed of molecules moving in random motion • Energy of all molecular motion is called internal energy per unit mass, e, of system • Only two ways e can be increased (or decreased): • Heat, dq, added to (or removed from) system • Work, dw, is done on (or by) system

5. 1st LAW IN MORE USEFUL FORM (4.5) • 1st Law: de = dq + dw • Find more useful expression for dw, in terms of p and r (or v = 1/r) • When volume varies → work is done • Work done on balloon, volume ↓ • Work done by balloon, volume ↑ Change in Volume (-)

6. ENTHALPY: A USEFUL QUANTITY (4.5) Define a new quantity called enthalpy, h: (recall ideal gas law: pv = RT) Differentiate Substitute into 1st law (from previous slide) Another version of 1st law that uses enthalpy, h:

7. HEAT ADDITION AND SPECIFIC HEAT (4.5) • Addition of dq will cause a small change in temperature dT of system dq dT • Specific heat is heat added per unit change in temperature of system • Different materials have different specific heats • Balloon filled with He, N2, Ar, water, lead, uranium, etc… • ALSO, for a fixed dq, resulting dT depends on type of process…

8. SPECIFIC HEAT: CONSTANT PRESSURE • Addition of dq will cause a small change in temperature dT of system • System pressure remains constant dq dT Extra Credit #1: Show this step

9. SPECIFIC HEAT: CONSTANT VOLUME • Addition of dq will cause a small change in temperature dT of system • System volume remains constant dq dT Extra Credit #2: Show this step

10. HEAT ADDITION AND SPECIFIC HEAT (4.5) • Addition of dq will cause a small change in temperature dT of system • Specific heat is heat added per unit change in temperature of system • However, for a fixed dq, resulting dT depends on type of process: Constant Pressure Constant Volume Specific heat ratio For air, g = 1.4

11. ISENTROPIC FLOW (4.6) • Goal: Relate Thermodynamics to Compressible Flow • Adiabatic Process: No heat is added or removed from system • dq = 0 • Note: Temperature can still change because of changing density • Reversible Process: No friction (or other dissipative effects) • Isentropic Process: (1) Adiabatic + (2) Reversible • (1) No heat exchange + (2) no frictional losses • Relevant for compressible flows only • Provides important relationships among thermodynamic variables at two different points along a streamline g = ratio of specific heats g = cp/cv gair=1.4

12. DERIVATION: ENERGY EQUATION (4.7) Energy can neither be created nor destroyed Start with 1st law Adiabatic, dq=0 1st law in terms of enthalpy Recall Euler’s equation Combine Integrate Result: frictionless + adiabatic flow

13. ENERGY EQUATION SUMMARY (4.7) • Energy can neither be created nor destroyed; can only change physical form • Same idea as 1st law of thermodynamics Energy equation for frictionless, adiabatic flow (isentropic) h = enthalpy = e+p/r = e+RT h = cpT for an ideal gas Also energy equation for frictionless, adiabatic flow Relates T and V at two different points along a streamline

14. SUMMARY OF GOVERNING EQUATIONS (4.8)STEADY AND INVISCID FLOW • Incompressible flow of fluid along a streamline or in a stream tube of varying area • Most important variables: p and V • T and r are constants throughout flow continuity Bernoulli continuity • Compressible, isentropic (adiabatic and frictionless) flow along a streamline or in a stream tube of varying area • T, p, r, and V are all variables isentropic energy equation of state at any point

15. EXAMPLE: SPEED OF SOUND (4.9) • Sound waves travel through air at a finite speed • Sound speed (information speed) has an important role in aerodynamics • Combine conservation of mass, Euler’s equation and isentropic relations: • Speed of sound, a, in a perfect gas depends only on temperature of gas • Mach number = flow velocity normalizes by speed of sound • If M < 1 flow is subsonic • If M = 1 flow is sonic • If M > flow is supersonic • If M < 0.3 flow may be considered incompressible

16. Streamline Stream tube Steady flow Unsteady flow Viscid flow Inviscid flow Compressible flow Incompressible flow Laminar flow Turbulent flow Constant pressure process Constant volume process Adiabatic Reversible Isentropic Enthalpy KEY TERMS: CAN YOU DEFINE THEM?

17. EXAMPLES AND APPLICATIONSMeasurement of AirspeedShock WavesSupersonic Wind Tunnels and Rocket Nozzles

18. MEASUREMENT OF AIRSPEED:SUBSONIC COMRESSIBLE FLOW • If M > 0.3, flow is compressible (density changes are important) • Need to introduce energy equation and isentropic relations cp: specific heat at constant pressure M1=V1/a1 gair=1.4

19. MEASUREMENT OF AIRSPEED:SUBSONIC COMRESSIBLE FLOW • So, how do we use these results to measure airspeed p0 and p1 give Flight Mach number Mach meter M1=V1/a1 Actual Flight Speed Actual Flight Speed using pressure difference What is T1 and a1? Again use sea-level conditions Ts, as, ps (a1=340.3 m/s)

20. EXAMPLE: TOTAL TEMPERATURE • A rocket is flying at Mach 6 through a portion of the atmosphere where the static temperature is 200 K • What temperature does the nose of the rocket ‘feel’? • T0 = 200(1+ 0.2(36)) = 1,640 K! Total temperature Static temperature Vehicle flight Mach number

21. MEASUREMENT OF AIRSPEED:SUPERSONIC FLOW • What can happen in supersonic flows? • Supersonic flows (M > 1) are qualitatively and quantitatively different from subsonic flows (M < 1)

22. HOW AND WHY DOES A SHOCK WAVE FORM? • Think of a as ‘information speed’ and M=V/a as ratio of flow speed to information speed • If M < 1 information available throughout flow field • If M > 1 information confined to some region of flow field

23. MEASUREMENT OF AIRSPEED:SUPERSONIC FLOW Notice how different this expression is from previous expressions You will learn a lot more about shock wave in compressible flow course

24. SUMMARY OF AIR SPEED MEASUREMENT • Subsonic, incompressible • Subsonic, compressible • Supersonic

25. HOW ARE ROCKET NOZZLES SHAPPED?

26. MORE ON SUPERSONIC FLOWS (4.13) Isentropic flow in a streamtube Differentiate Euler’s Equation Since flow is isentropic a2=dp/dr Area-Velocity Relation

27. CONSEQUENCES OF AREA-VELOCITY RELATION • IF Flow is Subsonic (M < 1) • For V to increase (dV positive) area must decrease (dA negative) • Note that this is consistent with Euler’s equation for dV and dp • IF Flow is Supersonic (M > 1) • For V to increase (dV positive) area must increase (dA positive) • IF Flow is Sonic (M = 1) • M = 1 occurs at a minimum area of cross-section • Minimum area is called a throat (dA/A = 0)

28. TRENDS: CONTRACTION 2: OUTLET 1: INLET M1 < 1 M1 > 1 V2 > V1 V2 < V1

29. TRENDS: EXPANSION 2: OUTLET 1: INLET M1 < 1 M1 > 1 V2 < V1 V2 > V1

30. PUT IT TOGETHER: C-D NOZZLE 2: OUTLET 1: INLET

31. MORE ON SUPERSONIC FLOWS (4.13) • A converging-diverging, with a minimum area throat, is necessary to produce a supersonic flow from rest Rocket nozzle Supersonic wind tunnel section

32. Chapter 5 Overview

33. 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

34. HOW DOES AN AIRFOIL GENERATE LIFT? • Flow velocity over top of airfoil is faster than over bottom surface • Streamtube A senses upper portion of airfoil as an obstruction • Streamtube A is squashed to smaller cross-sectional area • Mass continuity rAV=constant: IF A↓ THEN V↑ Streamtube A is squashed most in nose region (ahead of maximum thickness) A B

35. HOW DOES AN AIRFOIL GENERATE LIFT? • As V ↑ p↓ • Incompressible: Bernoulli’s Equation • Compressible: Euler’s Equation • Called Bernoulli Effect • With lower pressure over upper surface and higher pressure over bottom surface, airfoil feels a net force in upward direction → Lift Most of lift is produced in first 20-30% of wing (just downstream of leading edge) Can you express these ideas in your own words?

36. AIRFOILS VERSUS WINGS Why do airfoils have such a shape? How are lift and drag produced? NACA airfoil performance data How do we design? What is limit of behavior?

37. AIRFOIL THICKNESS: WWI AIRPLANES English Sopwith Camel Thin wing, lower maximum CL Bracing wires required – high drag German Fokker Dr-1 Higher maximum CL Internal wing structure Higher rates of climb Improved maneuverability

38. AIRFOIL NOMENCLATURE • Mean Chamber Line:Set of points halfway between upper and lower surfaces • Measured perpendicular to mean chamber line itself • Leading Edge:Most forward point of mean chamber line • Trailing Edge:Most reward point of mean chamber line • Chord Line:Straight line connecting the leading and trailing edges • Chord, c:Distance along the chord line from leading to trailing edge • Chamber:Maximum distance between mean chamber line and chord line • Measured perpendicular to chord line

39. NACA FOUR-DIGIT SERIES • First digit specifies maximum camber in percentage of chord • Second digit indicates position of maximum camber in tenths of chord • Last two digits provide maximum thickness of airfoil in percentage of chord Example: NACA 2415 • Airfoil has maximum thickness of 15% of chord (0.15c) • Camber of 2% (0.02c) located 40% back from airfoil leading edge (0.4c) NACA 2415

40. WHAT CREATES AERODYNAMIC FORCES? (2.2) • Aerodynamic forces exerted by airflow comes from only two sources: • Pressure, p, distribution on surface • Acts normal to surface • Shear stress, tw, (friction) on surface • Acts tangentially to surface • Pressure and shear are in units of force per unit area (N/m2) • Net unbalance creates an aerodynamic force “No matter how complex the flow field, and no matter how complex the shape of the body, the only way nature has of communicating an aerodynamic force to a solid object or surface is through the pressure and shear stress distributions that exist on the surface.” “The pressure and shear stress distributions are the two hands of nature that reach out and grab the body, exerting a force on the body – the aerodynamic force”

41. RESOLVING THE AERODYNAMIC FORCE • Relative Wind: Direction of V∞ • We use subscript ∞ to indicate far upstream conditions • Angle of Attack, a:Angle between relative wind (V∞) and chord line • Total aerodynamic force, R, can be resolved into two force components • Lift, L: Component of aerodynamic force perpendicular to relative wind • Drag, D: Component of aerodynamic force parallel to relative wind

42. MORE DEFINITIONS • Total aerodynamic force on airfoil is summation of F1 and F2 • Lift is obtained when F2 > F1 • Misalignment of F1 and F2 creates Moments, M, which tend to rotate airfoil/wing • A moment (torque) is a force times a distance • Value of induced moment depends on point about which moments are taken • Moments about leading edge, MLE, or quarter-chord point, c/4, Mc/4 • In general MLE≠ Mc/4 F1 F2

43. VARIATION OF L, D, AND M WITH a • Lift, Drag, and Moments on a airfoil or wing will change as a changes • Variations of these quantities are some of most important information that an airplane designer needs to know • Aerodynamic Center • Point about which moments essentially do not vary with a • Mac=constant (independent of a) • For low speed airfoils aerodynamic center is near quarter-chord point, c/4

44. AOA = 2°

45. AOA = 3°

46. AOA = 6°

47. AOA = 9°

48. AOA = 12°

49. AOA = 20°

50. AOA = 60°