Presentation on theme: "MAE 1202: AEROSPACE PRACTICUM"— Presentation transcript:
1 MAE 1202: AEROSPACE PRACTICUM Lecture 7: Compressible Flow Review and Overview of AirfoilsMarch 11, 2013Mechanical and Aerospace Engineering DepartmentFlorida Institute of TechnologyD. R. Kirk
2 UDPATES Mid-term grades Team project: Introduced in Laboratory this weekMid-Term Exam: Monday, March 18, 2013 in classCovers Chapter 4 and Chapter 5.1 – 5.7Open book / open notes… but no time to study during the examNo computers, cell phones, etc.Sample Mid-Term with Solution on lineReview Session: Thursday, March 14, 2013, Crawford Science Tower, Room 112, 8 – 10 pmAIAA Meeting/Fund Raiser Friday, March 15, 2013, 7:00 pm – 11:00 pm, Buffalo Wild Wings (Palm Bay Road)
3 READING AND HOMEWORK ASSIGNMENTS Reading: Introduction to Flight, by John D. Anderson, Jr.For March 25, 2013 lecture: Chapter 5, SectionsRead these sections carefully, most interesting portions of Ch. 5Lecture-Based Homework Assignment:Problems: 5.7, 5.11, 5.13, 5.15, 5.17, 5.19DUE: Friday, March 29, 2013 by 5pmTurn in hard copy of homeworkAlso be sure to review and be familiar with textbook examples in Chapter 5
4 ANSWERS TO LECTURE HOMEWORK 5.7: Cp = -3.915.11: Cp =Be careful here, if you check the Mach number it is around 0.71, so the flow is compressible and the formula for Cp based on Bernoulli’s equation is not valid. To calculate the pressure coefficient, first calculate r∞ from the equation of state and find the temperature from the energy equation. Finally make use of the isentropic relations and the definition of Cp given in Equation 5.275.13: cl = 0.97Make use of Prandtl-Glauert rule5.15: Mcr = 0.62Use graphical technique of Section 5.9Verify using Excel or Matlab5.17: m = 30°5.19: D = 366 lbRemember that in steady, level flight the airplane’s lift must balance its weightYou may also assume that all lift is derived from the wings (this is not really true because the fuselage and horizontal tail also contribute to the airplane lift). Also assume that the wings can be approximated by a thin flat plateRemember that Equation 5.50 gives a in radians
5 HOMEWORK EXAMPLESCan you read this?Who would you hire?
8 SUMMARY OF GOVERNING EQUATIONS (4.8) STEADY AND INVISCID FLOW Incompressible flow of fluid along a streamline or in a stream tube of varying areaMost important variables: p and VT and r are constants throughout flowcontinuityBernoullicontinuityCompressible, isentropic (adiabatic and frictionless) flow along a streamline or in a stream tube of varying areaT, p, r, and V are all variablesisentropicenergyequation of stateat any point
9 MEASUREMENT OF AIRSPEED: SUBSONIC COMRESSIBLE FLOW If M > 0.3, flow is compressible (density changes are important)Need to introduce energy equation and isentropic relationscp: specific heat at constant pressureM1=V1/a1gair=1.4
10 EXAMPLE: TOTAL TEMPERATURE Static temperatureVehicle flightMach numberA rocket is flying at Mach 6 through a portion of the atmosphere where the static temperature is 200 KWhat temperature does the nose of the rocket ‘feel’?T0 = 200(1+ 0.2(36)) = 1,640 K!
11 MEASUREMENT OF AIRSPEED: SUBSONIC COMRESSIBLE FLOW So, how do we use these results to measure airspeedp0 and p1 giveFlight Mach numberMach meterM1=V1/a1Actual Flight SpeedActual Flight Speedusing pressure differenceWhat is T1 and a1?Again use sea-level conditions Ts, as, ps (a1=340.3 m/s)
12 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)
13 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 speedIf M < 1 information available throughout flow fieldIf M > 1 information confined to some region of flow field
14 MEASUREMENT OF AIRSPEED: SUPERSONIC FLOW Notice how different this expression is from previous expressionsYou will learn a lot more about shock wave in compressible flow course
15 SUMMARY OF AIR SPEED MEASUREMENT Subsonic, incompressibleSubsonic, compressibleSupersonic
17 MORE ON SUPERSONIC FLOWS (4.13) Isentropic flow in a streamtubeDifferentiateEuler’s EquationSince flow is isentropica2=dp/drArea-Velocity Relation
18 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 dpIF 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-sectionMinimum area is called a throat (dA/A = 0)
24 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 generatedWhy 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
25 HOW DOES AN AIRFOIL GENERATE LIFT? Flow velocity over top of airfoil is faster than over bottom surfaceStreamtube A senses upper portion of airfoil as an obstructionStreamtube A is squashed to smaller cross-sectional areaMass continuity rAV=constant: IF A↓ THEN V↑Streamtube A is squashedmost in nose region(ahead of maximum thickness)AB
26 HOW DOES AN AIRFOIL GENERATE LIFT? As V ↑ p↓Incompressible: Bernoulli’s EquationCompressible: Euler’s EquationCalled Bernoulli EffectWith lower pressure over upper surface and higher pressure over bottom surface, airfoil feels a net force in upward direction → LiftMost of lift is producedin first 20-30% of wing(just downstream of leading edge)Can you express these ideas in your own words?
27 AIRFOILS VERSUS WINGS Why do airfoils have such a shape? How are lift and drag produced?NACA airfoil performance dataHow do we design?What is limit of behavior?
28 AIRFOIL THICKNESS: WWI AIRPLANES English Sopwith CamelThin wing, lower maximum CLBracing wires required – high dragGerman Fokker Dr-1Higher maximum CLInternal wing structureHigher rates of climbImproved maneuverability
29 AIRFOIL NOMENCLATUREMean Chamber Line: Set of points halfway between upper and lower surfacesMeasured perpendicular to mean chamber line itselfLeading Edge: Most forward point of mean chamber lineTrailing Edge: Most reward point of mean chamber lineChord Line: Straight line connecting the leading and trailing edgesChord, c: Distance along the chord line from leading to trailing edgeChamber: Maximum distance between mean chamber line and chord lineMeasured perpendicular to chord line
30 NACA FOUR-DIGIT SERIES First digit specifies maximum camber in percentage of chordSecond digit indicates position of maximum camber in tenths of chordLast two digits provide maximum thickness of airfoil in percentage of chordExample: NACA 2415Airfoil 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
31 WHAT CREATES AERODYNAMIC FORCES? (2.2) Aerodynamic forces exerted by airflow comes from only two sources:Pressure, p, distribution on surfaceActs normal to surfaceShear stress, tw, (friction) on surfaceActs tangentially to surfacePressure 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”
32 RESOLVING THE AERODYNAMIC FORCE Relative Wind: Direction of V∞We use subscript ∞ to indicate far upstream conditionsAngle of Attack, a: Angle between relative wind (V∞) and chord lineTotal aerodynamic force, R, can be resolved into two force componentsLift, L: Component of aerodynamic force perpendicular to relative windDrag, D: Component of aerodynamic force parallel to relative wind
33 MORE DEFINITIONSTotal aerodynamic force on airfoil is summation of F1 and F2Lift is obtained when F2 > F1Misalignment of F1 and F2 creates Moments, M, which tend to rotate airfoil/wingA moment (torque) is a force times a distanceValue of induced moment depends on point about which moments are takenMoments about leading edge, MLE, or quarter-chord point, c/4, Mc/4In general MLE ≠ Mc/4F1F2
34 VARIATION OF L, D, AND M WITH a Lift, Drag, and Moments on a airfoil or wing will change as a changesVariations of these quantities are some of most important information that an airplane designer needs to knowAerodynamic CenterPoint about which moments essentially do not vary with aMac=constant (independent of a)For low speed airfoils aerodynamic center is near quarter-chord point, c/4
43 SAMPLE DATA: SYMMETRIC AIRFOIL Lift (for now)Angle of Attack, aA symmetric airfoil generates zero lift at zero a
44 SAMPLE DATA: CAMBERED AIRFOIL Lift (for now)Angle of Attack, aA cambered airfoil generates positive lift at zero a
45 SAMPLE DATA Lift (for now) Cambered airfoil has lift at a=0 Lift coefficient (or lift) linear variation with angle of attack, aCambered airfoils have positive lift when a = 0Symmetric airfoils have zero lift when a = 0At high enough angle of attack, the performance of the airfoil rapidly degrades → stallLift (for now)Cambered airfoil haslift at a=0At negative a airfoilwill have zero lift
46 SAMPLE DATA: STALL BEHAVIOR Lift (for now)What is really going on hereWhat is stall?Can we predict it?Can we design for it?
47 REAL EFFECTS: VISCOSITY (m) To understand drag and actual airfoil/wing behavior we need an understanding of viscous flows (all real flows have friction)Inviscid (frictionless) flow around a body will result in zero drag!This is called d’Alembert’s paradoxMust include friction (viscosity, m) in theoryFlow adheres to surface because of friction between gas and solid boundaryAt surface flow velocity is zero, called ‘No-Slip Condition’Thin region of retarded flow in vicinity of surface, called a ‘Boundary Layer’At outer edge of B.L., V∞At solid boundary, V=0“The presence of friction in the flow causes a shear stress at the surface of a body, which, in turn contributes to the aerodynamic drag of the body: skin friction drag” p.219, Section 4.20
48 TYPES OF FLOWS: FRICTION VS. NO-FRICTION Flow very close to surface of airfoil isInfluenced by friction and is viscous(boundary layer flow)Stall (separation) is a viscous phenomenaFlow away from airfoil is not influencedby friction and is wholly inviscid
50 THE REYNOLDS NUMBER, Re Within B.L. flow Outside B.L. flow One of most important dimensionless numbers in fluid mechanics/ aerodynamicsReynolds number is ratio of two forces:Inertial ForcesViscous Forcesc is length scale (chord)Reynolds number tells you when viscous forces are important and when viscosity may be neglectedOutside B.L. flowInviscid (high Re)Within B.L. flowhighly viscous(low Re)
51 LAMINAR VS. TURBULENT FLOW Two types of viscous flowsLaminar: streamlines are smooth and regular and a fluid element moves smoothly along a streamlineTurbulent: streamlines break up and fluid elements move in a random, irregular, and chaotic fashion
52 LAMINAR VS. TURBULENT FLOW All B.L.’s transition from laminar to turbulentTurbulent velocityprofiles are ‘fuller’cf,turb > cf,lam
53 FLOW SEPARATIONKey to understanding: Friction causes flow separation within boundary layerSeparation then creates another form of drag called pressure drag due to separation
54 REVIEW: AIRFOIL STALL (4.20, 5.4) Key to understanding: Friction causes flow separation within boundary layerB.L. either laminar or turbulentAll laminar B.L. → turbulent B.L.Turbulent B.L. ‘fuller’ than laminar B.L., more resistant to separationSeparation creates another form of drag called pressure drag due to separationDramatic loss of lift and increase in drag
55 SUMMARY OF VISCOUS EFFECTS ON DRAG (4.21) Friction has two effects:Skin friction due to shear stress at wallPressure drag due to flow separationTotal drag due toviscous effectsCalled Profile DragDrag due toskin frictionDrag due toseparation=+Less for laminarMore for turbulentMore for laminarLess for turbulentSo how do you design?Depends on case by case basis, no definitive answer!
56 COMPARISON OF DRAG FORCES Same total drag as airfoil
57 TRUCK SPOILER EXAMPLE Note ‘messy’ or turbulent flow pattern High drag Lower fuel efficiencySpoiler angle increased by + 5°Flow behavior more closely resembles a laminar flowTremendous savings (< $10,000/yr) on Miami-NYC route
58 LIFT, DRAG, AND MOMENT COEFFICIENTS (5.3) Behavior of L, D, and M depend on a, but also on velocity and altitudeV∞, r ∞, Wing Area (S), Wing Shape, m ∞, compressibilityCharacterize behavior of L, D, M with coefficients (cl, cd, cm)Matching Mach and Reynolds(called similarity parameters)M∞, ReM∞, Recl, cd, cm identical
59 LIFT, DRAG, AND MOMENT COEFFICIENTS (5.3) Behavior of L, D, and M depend on a, but also on velocity and altitudeV∞, r ∞, Wing Area (S), Wing Shape, m ∞, compressibilityCharacterize behavior of L, D, M with coefficients (cl, cd, cm)Note on Notation:We use lower case, cl, cd, and cm for infinite wings (airfoils)We use upper case, CL, CD, and CM for finite wings
64 AIRFOIL DATA (5.4 AND APPENDIX D) NACA 1408 WING SECTION Flaps shift lift curveEffective increase in camber of airfoilFlap extendedFlap retracted
65 PRESSURE DISTRIBUTION AND LIFT Lift comes from pressure distribution over top (suction surface) and bottom (pressure surface)Lift coefficient also result of pressure distribution
66 PRESSURE COEFFICIENT, CP (5.6) Use non-dimensional description, instead of plotting actual values of pressurePressure distribution in aerodynamic literature often given as CpSo why do we care?Distribution of Cp leads to value of clEasy to get pressure data in wind tunnelsShows effect of M∞ on cl
68 COMPRESSIBILITY CORRECTION: EFFECT OF M∞ ON CP For M∞ < 0.3, r ~ constCp = Cp,0 = 0.5 = constM∞
69 COMPRESSIBILITY CORRECTION: EFFECT OF M∞ ON CP Effect of compressibility(M∞ > 0.3) is to increaseabsolute magnitude of Cp as M∞ increasesCalled: Prandtl-Glauert RuleFor M∞ < 0.3, r ~ constCp = Cp,0 = 0.5 = constM∞Prandtl-Glauert rule applies for 0.3 < M∞ < 0.7
71 COMPRESSIBILITY CORRECTION SUMMARY If M0 > 0.3, use a compressibility correction for Cp, and clCompressibility corrections gets poor above M0 ~ 0.7This is because shock waves may start to form over parts of airfoilMany proposed correction methods, but a very good on is: Prandtl-Glauert RuleCp,0 and cl,0 are the low-speed (uncorrected) pressure and lift coefficientsThis is lift coefficient from Appendix D in AndersonCp and cl are the actual pressure and lift coefficients at M∞
72 CRITICAL MACH NUMBER, MCR (5.9) As air expands around top surface near leading edge, velocity and M will increaseLocal M > M∞Flow over airfoil may havesonic regions even thoughfreestream M∞ < 1INCREASED DRAG!
74 CRITICAL FLOW AND SHOCK WAVES ‘bubble’ of supersonic flow
75 AIRFOIL THICKNESS SUMMARY Note: thickness is relativeto chord in all casesEx. NACA 0012 → 12 %Which creates most lift?Thicker airfoilWhich has higher critical Mach number?Thinner airfoilWhich is better?Application dependent!
76 AIRFOIL THICKNESS: WWI AIRPLANES English Sopwith CamelThin wing, lower maximum CLBracing wires required – high dragGerman Fokker Dr-1Higher maximum CLInternal wing structureHigher rates of climbImproved maneuverability
78 MODERN AIRFOIL SHAPES Boeing 737 Root Mid-Span Tip
79 SUMMARY OF AIRFOIL DRAG (5.12) Only at transonic andsupersonic speedsDwave=0 for subsonic speedsbelow Mdrag-divergenceProfile DragProfile Drag coefficient relatively constant with M∞ at subsonic speeds