Transcript

VISCOUS EFFECTS, THE BOUNDARY LAYER AND

FLOE SEPARATION
Skin Friction – Air resistance and it is the tangential component of
force on the surface of a body due to the friction between the two
particles.
Stream line and Turbulent flow – A stream line flow may be defined
as a smooth non turbulent flow. A turbulent flow is defined as a flow
characterized by turbulence, that is, a flow in which the velocity varies
erratically in both magnitude and direction with time.
Laminar flow – The word laminar is derived from the latin word
“lamina” meaning a thin plate of metal or some other material.
Laminar flows employs, the concept that air is flowing in thin sheets or
layers close to the surface of a wing with no disturbance between the
layers of air.
Boundary Layer – A boundary layer is that layer of air adjacent to the
airfoil surface. The cause of the boundary layer is the friction between
the surface of the wing and the air.
Laminar Boundary Layer – Is the laminar boundary layers the flow is
steady and smooth. As a result, the layer is very thin and so the form
drag is very small. Also, the velocity gradient at the walls through
large enough to give significant viscous stress is yet only moderate, so
that the skin friction, though not negligible, is also very small.

 
 
 
 
 
The rubbing of the boundary layer on the flat plate gives rise to
friction forces of: friction drag. The skin friction drag coefficient for
one side of a plate in laminar flow is given by:
 
 
 
 

Turbulent Boundary Layer – In a turbulent boundary layer, the flow
is unsteady and not smooth, but eddying.
When the flow is transitioned to turbulent flow, the boundary layer
thickness will be increased. In fact, this phenomenon is often used to
determine the location of the transition region. The boundary layer
thickness can be determined by:
 

The skin friction drag coefficient for a flat plate can be calculated with
formula:
 
 
 
 

Critical Raynolds Number – Experimentally value for which when
the values of R.N. less than critical, the flow is smooth or laminar; for
values greater than the critical R.N., the flow is turbulent.
Transition takes place on a flat plate at point x determined by:
 
 
 
 
 
 
 
 

For air µ increases with temperature and can be calculated by the
following approximate formula for the standard atmosphere.
 
Or
 

The free stream velocity for the smaller plate is 100ft per sec.   Large plate Small plate     . one having 6 ft span and 3 ft chord. the other having 9ft span and 6ft chord are placed in different airstream. It is found that the total skin friction drag for the two plate is the same.Example # 1: Two plates. Find the airspeed for the larger plate. Assume the laminar flow at  standard sea level conditions.

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If the wing chord is 6ft and the equivalent airspeed is 200knots. What is the overall Raynolds number of the wing?                   .Example # 2: An airplane is flying at a density altitude of 15.000ft. At an ambient temperature a -39ᵒF.

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WIND TUNNEL A device for testing aircraft and its force components in a controlled airstream under laboratory conditions. TYPES OF LOW-SPEED WIND TUNNELS OPEN-CIRCUIT WIND TUNNELS .

CLOSED CIRCUIT TUNNEL .

) Noise is significantly lower. 3. 5.) Laboratory air movement (air vents. 2.) Power Requirement for a given speed is lower.) Air entering the test section is free of laboratory dust.) Particulate matter can be contained within the circuit. etc.Advantages of Closed circuit with comparison with Open Circuit Tunnels 1. 4. . windows.) Fan blades are not as vulnerable to damage from model failure. 6.) does not affect wind tunnel flow. doors.

) Increasing air temperature can become an issue during prolonged use.) Footprint is much larger and requires more overall space. 2.Disadvantages of Closed circuit with Open Circuit Tunnels 1.) Air supply is recycled which can be prohibitive when working with combustion engines. 4. . 3.) Cost is generally three times greater for a given test section size.

) Side Force 4.FORCES AND MOTION OF AIRPLANE UNDER TESTING 1.) Drag 3.) Lift 2.) Pitching Moment 5.) Yawing Movement 6.) Rolling Movement .

) Direction of flow is the same. 4. .) Magnitude of velocity at constant proportion.) Both bodies must be positioned at the same angle of attack. 2.Importance   of Used in comparison on flow pattern of on theorem bodies which are geometrically similar but not in dimension.) Both bodies must be oriented or positioned in similar altitudes. Flow pattern similarity at a particular point 1. 3.

moving at 130mph through standard atmosphere.                     .Example # 1: Find the Raynold Number for an airplane wing 4ft chord.

                    .Example # 2: Find the Raynold Number for an airplane wing with 3ft 6inches chord moving at 180mph through standard air.

Air is +40°C.                   . barometer. moving at 150mph. 4ft chord.Example # 3: Find the Raynold Number for an airplane wing.21in Hg.

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Air under  standard conditions in both cases.                               .Example # 4: Find the velocity at which test should be run in a wind tunnel on a model wing of 4in chord in order that the Raynold Number shall be the same as for a wing with 4 ft chord at 100mph.

air velocity being 60mph in order that the Raynold Number shall be the same as for the full size wing of 4ft chord.                               . moving at 100mph through the air? Air  temperatures are the same in each case.Example # 5: In a variable density wind tunnel. chord. what pressure should test be run on a model with a 3in.

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Variable Density Wind Tunnel A wind tunnel in which the air density can be increased by means of compressed air. Flat Plates Flat plates perpendicular to the airstream             .

Example# 1: What is the total force of a 45mph wind on a hangar door 40ft by 25ft?                     .

Example # 2: What is the force against the side of the building 70ft long and 40ft high in a 90mph wind?                   .

Example # 3: What force is required to push a flat plate. 3ft by 2ft at a speed of 35 fps in a direction perpendicular to its surface?                   .

What is the force against the windshield at 60mph?                   .Example # 4: An auto windshield is 40in wide by 15in high and is vertical.

Curved Deflecting Surfaces     The Resultant of these two components is     .

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  Example # 1: A stream of air 50 ft wide and 10 ft high is moving horizontally at a speed of 60mph. What is the magnitude of these force required to deflect it movement 4downward without loss in speed?                     .

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What force is required to deflect it downward 10 without loss in speed?                     .  Example # 2: A stream of air 72 sq ft in cross section is moving horizontally at a speed of 100mph.

What force is required to deflect it downward 8deg?                     .Example # 3: A stream of air 60ft wide and 8ft high is moving horizontally at a speed of 75mph.

Example # 4: A stream of air 100sq. in cross section is moving horizontally at a speed of 150mph. What is total force against the cylinder?                     .ft. It strikes tangentially against the interior wall of semi-circular cylinder so that it is deflected through 180°.

AIRFOIL THEORY Airfoil-is a streamline body which when set at a suitable angle of attack produces more lift than drag. . elevator. aileron. Any surface such as an airplane wing.

DEFINITION OF AIRFOIL GEOMETRY Mean Camber Line – is the line joining the midpoints between the upper and lower surfaces of an airfoil and measured normal to the mean camber line. Thickness – Is the height of measured normal to the chordline. Leading Edge Radius – Is the radius of a circle tangent to the upper and lower surfaces. with its center located on a tangent to the mean camber line drawn through the leading edge of this line. profile maximum Camber – Is the maximum distance of the mean camber line from the chordline..  Thickness Ratio – Is the thickness to the chord ratio. Chord Line – Is the line joining the end points of the mean camber line. .

DEFINITION OF SECTION FORCES AND MOMENT FACTORS AFFECTING THE AERODYNAMIC FORCES 1.) Air density.) Velocity of air. V 2.) Characteristic area or size. S 4. � 5.)  Speed of sound.) Coefficient of dynamic viscosity.(compressibility effect). . ρ 3.

FORMULAS Lift Force   Where:     Drag Force   Pitching Moment       .

Important Airfoil Characteristics The following relationship are of fundamental importance to airplane design and airplane analysis. curve can be represented         Where “a” or is the lift curve slope and the angle of attack for zero lift.   The linear portion of the lift mathematically by the equation. The theoretical value of “a” is 2π per radian.     .

according Bernoulli Equation.   At low speeds.   to the incompressible .AIRFOIL PRESSURE DISTRIBUTION   The pressure distribution is normally expressed in terms of the pressure coefficient.

Critical Pressure Coefficient   Critical Pressure Is the local pressure at the point in the air flow where M=1.   Critical Velocity   .0 and the velocity is critical.

000ft.Example # 1: An Airplane is flying at 480mph at an altitude of 30.What is the critical Velocity?                                 .

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What is the critical Velocity?                 .Example # 2: An Airplane is flying at 500knots in air at -50°F.

                  .Example # 3: What is the critical value of pressure and pressure coefficient for an airplane flying at 500knots in air at 25°F.

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At what angle of attack will the airfoil developed a lift of 140 lb/ft at 100mph under standard sea level  condition. Assume c=8ft.Example # 4: An airfoil has a lift curve slope of 6.3 per radian and angle of attack zero lift of -2°.                                     .

04c 4=Position of the camber at 0.E.NACA AIRFOILS DESIGNATION 4 –DIGIT AIRFOILS: Example NACA 4412 4=Camber 0. 12=Maximum thickness 0.12c 5-DIGIT AIRFOILS: Example NACA 23012 2=camber 0.15 times the first digit for 30=position   this seriesof camber at =0.4c from L.02c =design lift coefficient is 0.12c .15c 12=Maximum thickness 0.

21c .NACA AIRFOILS DESIGNATION -SERIES AIRFOILS: Example NACA 653-421 6=series designation 5=min.5c 3=The drag coefficient is near its minimum value over a range of lift coefficient of 0.3 above and below the design lift coefficient. 4=design lift coefficient 0. thickness 0.4 21=max. pressure at 0.

7c at the design lift coefficient.E. to 0. A=a serial letter to distinguish different section having the same numerical designation but different mean line or thickness distribution.NACA AIRFOILS DESIGNATION 7-SERIES AIRFOILS: Example NACA 747A315 7=series designation 4=favourable pressure gradient on the upper surface from L.3 15=max thickness 0. 7=favourable pressure gradient on the lower surface from L.E. 3=design lift coefficient 0.15c .7c at the design lift coefficient. to 0.

find the camber. thickness.Example # 1: NACA 4412.                                 . c=100cm. position of camber and max.

position of camber and max. thickness..c=48 in.Example # 2: NACA 23015. find the camber.                                   .