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Mechanics of Flight/Fundamentals of Flight COURSE NOTES

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  1. Mechanics of Flight/Fundamentals of FlightCOURSE NOTES John Baird

  2. MILESTONES IN FLIGHT • GEORGE CAYLEY (1773 - 1857): WAS THE FIRST TO EXPLAIN HOW THE FORCE ON THE WIN CAN BE RESOLVED INTO TWO COMPONENTS OF LIFT PERPENDICULAR TO THE FLIGHT DIRECTION DRAG PARALLEL TO THE FLIGHT DIRECTION LIFT WING SURFACE DRAG CAYLEY ALSO UNDERSTOOD THE FIRST PRINCIPLES OF STABILITY AND CONTROL

  3. WE TRY TO ANSWER THE THREE BASIC QUESTIONS 1. WHY AN AEROPLANE FLIES? AERODYNAMICS 2. WHY DOES IT FLY - SO FAST? SO FAR? SO HIGH? PERFORMANCE 3. WHY DOES IT BEHAVE THE WAY IT DOES AND HOW TO CONTROL IT? STABILITY & CONTROL

  4. Visualisation Examples

  5. VISCOSITY VISCOSITY TWO FEATURES OF LIQUIDS AND GASES ARE RESPONSIBLE FOR EXISTENCE OF COHESIVE OR ATTRACTIVE FORCES DOMINATE OVER INERTIA FORCES AND LARGER THE COHESIVE FORCES (MORE CLOSELY PACKED MOLECULES, GREATER THE VISCOSITY. LIQUIDS THE BASIS OF VISCOSITY IS THE INTERNAL RESISTANCE DUE TO COLLISION AND TRANSFER OF MOMENTUM. GASES Fast molecules exchange with slow ones and vice versa. Slowing of fast molecules and vice versa is viscosity. Fast drift Slow drift

  6. FOR LIQUIDS • VISCOSITY WITH TEMP. BECAUSE BONDS BETWEEN MOLECULES WEAKEN OR CAN EVEN BREAK IN OTHER WORDS, COHESIVE FORCES WEAKEN. • VISCOSITY WITH TEMP. BECAUSE INCREASE IN TEMPERATURE CAUSES INCREASED MOLECULAR ACTIVITY WHICH IN TURN LEADS TO MORE COLLISIONS AND MORE TRANSFER OF MOMENTUM, THEREFORE MORE VISCOSITY. DECREASES FOR GASES INCREASES

  7. NEWTON’S LAW OF VISCOSITY u2 • THIS ESTABLISHES THE RELATION BETWEEN SHEAR FORCE (FRICTION FORCE) AND THE VISCOSITY. • IT STATES SHEARING FORCE A AREA OF INTERFACE u VELOCITY DIFFERENCE BETWEEN ADJACENT LAYERS OF FLUID. h SEPARATION DISTANCE BETWEEN LAYERS OF FLUID  PROPORTIONALITY CONST. CALLED THE COEFFICIENT OF VISCOSITY. Fs h u1 u = u2- u1 Fs

  8. DEFINITION OF VELOCITY GRADIENT Moving plate u A Couette or channel flow A’ h B’ B u  Fixed plate gradient u=0 Flow velocity gradient Boundary layer flow y B A Fixed plate velocity profile

  9. UNITS OF SHEAR STRESS ARE N/m2 in SI. FLUIDS OBEYING NEWTON’S LAW, ARE CALLED Newtonian Fluids EXAMPLES : AIR, WATER, ALL FLUIDS WHICH HAVE SIMPLE MOLECULAR STRUCTURE. THINK OF SOME FLUIDS WHICH ARE NOT NEWTONIAN!

  10. International Standard Atmosphere 30 Balloons Ozone Layer Mesosphere U2 Spyplane 20 Concorde Stratosphere Altitude (km) Large Jet Liners Tropopause 10 Troposphere General Aviation Helicopters Birds Sea Level Insects -56.5 Temperature (degrees Centigrade)

  11. SPEED OF SOUND • THE SPEED OF SOUND IS RELATED TO THE PRESSURE & DENSITY BY THE ISENTROPIC RELATION • WHERE  IS THE RATIO OF SPECIFIC HEATS IN AIR (CP/ CV) AND IS EQUAL TO 1.4 • NOTE THAT THE SPEED OF SOUND IS A FUNCTION OF TEMPERATURE. THE SPEED OF SOUND DECREASES WITH INCREASING ALTITUDE (IE DECREASING TEMPERATURE) • R IS THE GAS CONSTANT FOR AIR AND IS 287.05 J/kg K

  12. PROPERTIES OF FLUIDS • FLUIDS CAN BE CLASSIFIED AS OR . • IN A COMPRESSIBLE FLUID, PRESSURE & VELOCITY CHANGES ARE ACCOMPANIED BY SIGNIFICANT DENSITY CHANGES. • IN AN INCOMPRESSIBLE FLUID, PRESSURE & VELOCITY CHANGES DO NOT CAUSE ANY APPRECIABLE CHANGES IN DENSITY. • LIQUIDS ARE GENERALLY INCOMPRESSIBLE (Eg. WATER). • GASES ARE GENERALLY COMPRESSIBLE (Eg. AIR). COMPRESSIBLE INCOMPRESSIBLE

  13. PROPERTIES OF FLUIDS • THE FLOW PARAMETER THAT BECOMES IMPORTANT UNDER SUCH CIRCUMSTANCES IS THE MACH NO. DISCUSSED EARLIER. • AT HIGH SPEEDS THEREFORE, WE CAN TALK IN TERMS OF: SUBSONIC 0.3 < M < 0.7 TRANSONIC 0.7 < M < 1.4 SUPERSONIC 1.4 < M < 5 HYPERSONIC M > 5

  14. FLOW REGIMES IN AIR TERMINOLOGY Subsonic Transonic Supersonic Hypersonic 0 1 2 3 4 5 6 7 8 9 10 Non Linear Oxygen dissociates (Chemical reactions important) Incompressible Linear Compressible 0 1 2 3 4 5 6 7 8 9 10

  15. BOUNDARY LAYERS IN VISCOUS FLOWS THE EFFECTS OF VISCOSITY (WHICH PRODUCE FRICTIONAL OR SHEAR STRESSES) ARE CONFINED TO A VERY THIN LAYER OF FLUID CLOSE TO THE SURFACE. THIS THIN LAYER NEAR THE SURFACE IN WHICH VISCOSITY EFFECTS ARE CONFINED IS CALLED BOUNDARY LAYER, BECAUSE OF INTERNAL FRICTION DUE TO VISCOSITY, THE LAYER OF AIR CLOSEST TO THE BODY ‘STICKS’ TO THE SURFACE AND THE VELOCITY GRADUALLY INCREASES TILL AT THE ‘EDGE’ OF THE BOUNDARY LAYER, IT IS EQUAL TO THE VELOCITY IN THE ADJACENT EXTERNAL FLOW. BOUNDARY LAYER DETAIL Flow BOUNDARY LAYER velocity gradient y B A Fixed plate velocity profile

  16. BOUNDARY LAYERS • BECAUSE THE EFFECTS OF VISCOSITY ARE CONFINED TO THE BOUNDARY LAYER, IT HAS OFTEN BEEN POSSIBLE TO ANALYSE AERODYNAMIC PROBLEMS BY TREATING THE AIR AS IDEAL FLUID AND THIS HAS YIELDED QUITE ACCEPTABLE RESULTS ESPECIALLY AS REGARDS . • FOR TREATING THE PROBLEM OF AERODYNAMIC DRAG, HOWEVER, WE NEED TO CONSIDER THE • WE ALSO NOTE THAT IN AN IDEAL FLUID, THAT HAS NO VISCOSITY, THE FLUID EXHIBITS NO SHEAR FORCES AND THERE WOULD BE NO RELATIVE MOTION BETWEEN ADJACENT LAYERS OF FLUID. SUCH A FLUID IS SAID TO PAST THE SURFACE. AERODYNAMIC LIFT BOUNDARY LAYER SLIP

  17. Velocity y BOUNDARY LAYERS • WITH REAL FLUIDS, ON THE OTHER HAND, THERE IS NO RELATIVE MOTION AT THE SURFACE. IN OTHER WORDS, AT THE SURFACE WE HAVE CONDITION. • THE CONCEPT OF THE BOUNDARY LAYER WAS FIRST PROPOSED BY THE GERMAN AERODYNAMICIST LUDWIG PRANDTL (1875 - 1953) IN 1905. • IT WAS TRULY A MILESTONE IN AERODYNAMICS NOSLIP Zero velocity at wall, the no slip condition

  18. TYPICAL BOUNDARY LAYER PROFILE Free stream velocity, U 0.99U  Boundary layer thickness Velocity gradient Velocity Profile Surface

  19. BOUNDARY LAYER BEHAVIOUR WHEN THE BOUNDARY LAYER IS SUBJECTED TO INCREASING PRESSURE IN THE FLOW DIRECTION, IT BECOMES MORE AND MORE SLUGGISH AS IT HAS TO FLOW AGAINST AN ADVERSE PRESSURE GRADIENT. IT EVENTUALLY COMES OFF THE SURFACE. THE BOUNDARY LAYER IS THEN SAID TO BE SEPARATED. WHEN THE BOUNDARY LAYER ON AN AEROFOIL OR WING SEPARATES, WE SAY THAT THE AEROFOIL OR WING HAS ONCE THE BOUNDARY LAYER SEPARATES THE DRAG INCREASES DRAMATICALLY AND WE CAN NO LONGER ASSUME THAT FLOW OVER. THE AEROFOIL IS SMOOTH (IDEAL). STALLED

  20. A Separated Boundary Layer

  21. B.L. BEHAVIOUR IN ADVERSE PRESSURE GRADIENT Pressure force Flow decelerating Flow separated Point of separation Increasing Pressure

  22. PRESSURE DISTRIBUTION ON AN AEROFOIL Negative pressure Adverse Pressure Gradient

  23. STALL ON AN AEROFOIL NOTE RECIRCULATION REGION Negative Pressure

  24. NATURE OF DRAG DRAG ARISES DUE TO PRESSURE DISTRIBUTION OVER BODY SKIN FRICTION ON SURFACE OF BODY SKIN FRICTION DRAG PRESSURE DRAG (ALSO CALLED FORM DRAG)

  25. V V REAL FLOWS AND AERODYNAMIC DRAG INCISCID FLOW VISCOUS FLOW

  26. Pressure Drag on a Cylinder degrees

  27. Skin Friction Drag y Skin Friction Drag= Area x Shear Stress at wall

  28. Total Drag DRAG ON A TWO DIMENSIONAL OBJECT (PROFILE DRAG) IS A COMBINATION OF PRESSURE DRAG (ALSO CALLED FORM DRAG) AND SKIN FRICTION DRAG PROFILE DRAG = PRESSURE DRAG + SKIN FRICTION DRAG

  29. Stream Tube VELOCITY IS INVERSELY PROPORTIONAL TO THE CROSS- SECTIONAL AREA. IN OTHER WORDS, WHENEVER THERE IS ACCELERATION OF FLUID FLOW, THE CROSS-SECTION IS NARROW AND THE STREAMLINES CONVERGE. WHEN THERE IS A DECELERATION, THE CROSS-SECTION IS WIDER AND THE STREAMLINES DIVERGE.

  30. Bernoulli’s Equation BERNOULLI’S EQN. RELATES CHANGES IN VELOCITY TO CHANGES IN PRESSURE IN STEADY INCOMPRESSIBLE INVISCID FLOW ALONG A STREAM LINE. IT IS THE MOST IMPORTANT EQUATION IN FLUID MECHANICS. where p is the (static) pressure  is the density, V is the local velocity and p0, the constant, is called the total pressure. The term is sometimes called the dynamic pressure.

  31. Applications of Bernoulli’s Equation One way of writing Bernoulli’s equation is: Total pressure = static pressure + dynamic pressure. A PITOT TUBE If the velocity is zero the pressure is equal to the total pressure 4d d To differential pressure gauge p

  32. Measurement of Velocity: FROM BERNOULLI’S EQN. WE HAVE THEREFORE, BY MEASURING THE DIFFERENCE BETWEEN THE TOTAL PRESSURE (Po) AND STATIC PRESSURE (), WE CAN CALCULATE THE VELOCITY IN A FLOW.

  33. PITOT TUBE USED IN A WIND TUNNEL TO MEASURE VELOCITY Test Section po V Pitot-static tube To micromanometer

  34. PITOT TUBE USED TO MEASURE BOUNDARY LAYER PROFILE V Boundary layer velocity profile Pitot tube fixed to manometer traverse Static orifice To manometer

  35. ALTERNATIVE VIEW OF BERNOULLI’S EQUATION pressure energy per unit volume Total energy per unit volume kinetic energy per unit volume

  36. Pressure and Velocity

  37. Using Bernoulli’s Equation to Measure Velocity of Aircraft THEREFORE, BY NOTING THE EQUIVALENT AIRSPEED FROM ASI AT ANY ALTITUDE, WE CAN DETERMINE THE TRUE AIR SPEED BY THE KNOWLEDGE OF RELATIVE DENSITY . USUALLY, THE AIRSPEED INDICATOR IS CALIBRATED SO THAT IT READS DIRECTLY THE SPEED EITHER IN KNOTS OR km/hr. Static pressure measured by port on fuselage Dynamic pressure measured by pitot probe

  38. Flow Examples Dividing streamline p=p0 at stagnation point Flow accelerates and pressure reduced

  39. Flow Examples All objects in a flow have a stagnation point

  40. Flow Examples s T s’ Free stream Vp Vp F F’ s’ s Pressure and Velocity V V p p Distance along aerofoil

  41. Smooth entry Control valve Dye filament V Water d (a) Laminar Flow Filament becomes unstable V Filament breakup and turbulent flow (b) Turbulent Flow TRANSITION TO TURBULENCE Osborne Reynolds in the 1880s investigated the behaviour of flow that was either direct (laminar) or sinuous (turbulent).

  42. Transition to Turbulence Whether the flow is turbulent or laminar depends on the relative magnitude of the viscous forces and the kinetic forces (momentum) of the flow. When viscous forces are large, small irregularities are removed by ‘viscous damping’. This is characterised by slow flow, and/or high viscosity. When the flow has sufficient momentum such that the viscous forces are relatively small, it becomes turbulent.

  43. Example of a Turbulent Boundary Layer

  44. Stability of Shear Flow V P p,V1 V P V P p,V2 V P Dividing stream line Splitter Plate Consider the flow above in which viscosity is very small. Consider what happens if the dividing stream line is disturbed a small amount. Note that, if the velocity difference is high enough the pressure differences will act to increase the divergence of the streamline. IT WILL BECOME TURBULENT

  45. Stability of Shear Flow U P p,U1 U P D U P p,U2 U P IF VISCOUS FORCES DOMINATE, DISTURBANCE ENERGY WILL DISSIPATE. IF KINETIC FORCES DOMINATE THE DISTURBANCES WILL GROW AND FLOW WILL BECOME TURBULENCE. WHETHER A FLOW IS TURBULENT OR NOT DEPENDS ON: = REYNOLDS NUMBER

  46. REYNOLDS NUMBER  = FLUID DENSITY V = A VELOCITY - USUALLY THE FREE STREAM VELOCITY D = A REPRESENTATIVE LENGTH SCALE  = THE FLUID VISCOSITY EXAMPLES U D CHORD C For a given configuration and definition the Re determines when the transition to turbulence occurs.

  47. LAMINAR AND TURBULENT FLOW LAMINAR FLOW SMOOTH STEADY SMALLER SHEAR STRESS TYPICALLY STREAMLINED BODIES LESS SKIN FRICTION DRAG. MORE PRESSURE DRAG Laminar profile Turbulent mean profile

  48. LAMINAR AND TURBULENT FLOW TURBULENT FLOW HIGHLY DISORGANISED BASICALLY LARGE UNSTEADY SHEAR STRESS MORE SKIN FRICTION DRAG. LESS PRESSURE DRAG TYPICALLY BLUFF BODIES Laminar profile Turbulent mean profile

  49. Transition to Turbulence Smoke visualisation of a boundary layer. The laminar boundary layer on the left is ‘tripped’ by a grid and becomes turbulent

  50. Boundary Layer Profiles Laminar Profile Y Streamlines Turbulent Profile Momentum exchange by viscous forces only U Momentum exchanged more effectively by mass transport into lower layers