UNIVERSITY OF SALFORD SCHOOL OF COMPUTING, SCIENCE AND ENGINEERING
AERODYNAMIC AERODYNAMIC CHARACTERISTIC OF A SLENDER WING – WING – BODY CONFIGURATION AT HIGH INCIDENCE
MOHAMED A ELIAS AERODYNAMICS DR. L. JOHNSTON SUBMISSION DATE: 11/11/2011 AEROSPACE ENGINEERING ENGINEERING
CONTENT
INTRODUCTION
The aim of this experiment is to understand the behaviour of the non-linear aerodynamic characteristic of a slender wing-body by changing the incidence angle over period of time. This experiment will elaborate further study on vortex separation flow over highly-swept sharp leading-edge wing and the results obtained from this experiment will then be compared using the FOTRAN application for vortex-lattice computational method.
APPARATUS
Slender body – the missile shaped body with the wing cropped-delta configuration is used in the wind tunnel to test the experiment. Wind tunnel- is used to carry out the experiment to measure the lift forces, drag forces and pitching moments. Force balance system – is used to hold the slender body onto the wind tunnel in order to rotate at different angle of attack. Betz Manometer – in order to measure the air pressure in working section Data Logger – to get all the experiments readings Thermometer – to record the temperature in the working section Voltmeter – is used to read voltage variation output for lift, drag and pitching moment.
GEOMETRIC CHARACTERISTIC OF WING
Leading-Edge Sweep Angle: ∆ L.E
70˚
¼ Chord Sweep Angle
64.1022˚
Root Chord
0.437m
Tip Chord
0.08m
Wing Span: S
0.26m
Zero – Lift Incidence Angle: α L=0
0˚
Mean Aerodynamic Chord: C mac
0.2996m
PROCEDURES
Missile shaped slender wing body is tested into a low speed wind tunnel at zero incidence angle and gradually changed from negative to positive incidence angle of attack, in order to measure the lift, drag and pitching moment at different ranges. Vortex lattice method is used to predict the coefficient of lift and coefficient of drag and the results obtained are compared with the experiment. Further the Polhamus’ leading-edge suction analogy was used to calculate the coefficient of lift and coefficient of drag and the same was compared with the experimental results and the vortex lattice method’s results. The following are the steps carried out to perform the experiment:
The model was placed into the wind tunnel
The wind tunnel was switched on and set to 700RPM
Incidence angle was then set to -14˚
Record the Temperature for the working section
Note down the readings of the voltages form the data logger for the lift, drag and pitching moment.
Repeat these measurements by varying the angle of attack from -14 to 28 degrees with the increment of 2.
After the final set of measurement record the temperature of the working section. Finally record the atmospheric pressure using the barometer.
THEORY
Aerodynamics is the branch of physics that deals with the motion of air and other gaseous fluids and with the forces acting on bodies passing through such a fluid. Aerodynamics seeks, in particular, to explain the principles governing the flight of aircraft, rockets, and missiles. Aerodynamic forces are generated and act on a rocket as it flies through the air. Forces are vector quantities having both a magnitude and a direction. The magnitude of the aerodynamic forces depends on the shape, size and velocity of the rocket and some properties of the air through which it flies. By convention, the single aerodynamic force is broken into two components: the drag force which is opposed to the direction of motion, and the lift force which acts perpendicular to the direction of motion. The lift and drag act through the centre of pressure which is the average location of the aerodynamic forces on an object. Aerodynamic forces are mechanical forces. They are generated by the interaction and contact of a solid body with a fluid, a liquid or a gas. Aerodynamic forces are not generated by a force field, in the sense of the field, or an electromagnetic field. For lift and drag to be generated, the rocket must be in contact with the air. So outside the atmosphere there is no lift and no drag. Aerodynamic forces are generated by the difference in velocity between the rocket and the air. There must be motion between the rocket and the air. If there is no relative motion, there is no lift and no drag. Aerodynamic forces are more important for a model rocket than for a full scale rocket because the entire flight path of the model rocket takes place in the atmosphere. A full scale rocket climbs above the atmosphere very quickly. Aerodynamic forces are used differently on a rocket than on an airplane. On an airplane, lift is used to overcome the weight of the aircraft, but on a rocket, thrust is used in opposition to weight. Because the centre of pressure is not normally located at the centre of gravity of the rocket, aerodynamic forces can cause the rocket to rotate in flight. The lift of a rocket is a side force used to stabilize and control the direction of flight. While most aircraft have a high lift to drag ratio, the drag of a rocket is usually much greater than the lift. We can think of drag as aerodynamic friction, and one of the sources of drag is the skin friction between the molecules of the air and the solid surface of the moving rocket. Because the skin friction is an interaction between a solid and a gas, the magnitude of the skin friction depends on properties of both solid and gas. For the solid, a smooth, waxed surface produces less skin friction than a roughened surface. For the gas, the magnitude depends on the viscosity of the air and the relative magnitude of the viscous forces to the motion of the flow, expressed as the Reynolds number. Along the surface, a boundary layer of low energy flow is generated and the magnitude of the skin friction depends on the state of this flow. We can also think of drag as aerodynamic resistance to the motion of the object through the fluid. This
source of drag depends on the shape of the rocket and is called form drag. As air flows around a body, the local velocity and pressure are changed. Since pressure is a measure of the momentum of the gas molecules and a change in momentum produces a force, a varying pressure distribution will produce a force on the body. We can determine the magnitude of the force by integrating or adding up the local pressure times the surface area around the entire body. The base area of a model rocket produces form drag. Lift occurs when a flow of gas is turned by a solid object. The flow is turned in one direction, and the lift is generated in the opposite direction, according to Newton's third law of action and reaction. For a model rocket, the nose cone, body tube, and fins can turn the flow and become a source of lift if the rocket is inclined to the flight direction. Factors Affecting the Aerodynamic behaviour: The Object -
Geometry has a large effect on the aerodynamic forces generated by an object. Lift and drag depend linearly on the size of the object moving through the air. The crosssectional shape of an object determines the form drag created by the pressure variation around the object. If we think of drag as aerodynamic friction, the amount of drag depends on the surface roughness of the object; a smooth, waxed surface produces less drag than a roughened surface. This effect is called skin friction and is usually included in the measured drag coefficient of the object. Motion of the Air -
Lift and drag are associated with the movement of the rocket through the air, so lift and drag depend on the velocity of the air. Lift and drag actually vary with the square of the relative velocity between the object and the air. The inclination of the object to the flow also affects the amount of lift and drag generated by a given shaped object. If the object moves through the air at speeds near the speed of sound, shock waves are formed on the object which create an additional drag component called wave drag. The motion of the object through the air also causes boundary layers to form on the object. A boundary layer is a region of very low speed flow near the surface which contributes to the skin friction. Properties of the Air -
Lift and drag depend directly on the mass of the flow going past the rocket. The drag also depends in a complex way on two other properties of the air: its viscosity and its compressibility. These factors affect the wave drag and skin frictions which are described above. We can gather all of this information on the factors that affect lift and drag into two mathematical equations called the Lift Equation and the Drag Equation. With these equations we can predict how much aerodynamic force is generated by a given body moving at a given speed through a given fluid.
CALCULATION
Most of the calculations for the experiment were carried out in Excel Spread-sheet, using the equation below. However there are some calculation solved, which are shown below. Dynamic Pressure in Working Section
q = 100 K1 x Betz (mbar) N/m
2
2
= 1.175 x Betz (N/m ) Force and Moment Coefficient
Coefficient of Lift CL:
whereby: L = Lift q = Dynamic pressure S = Wing Span
Coefficient of Drag CD:
Coefficient of Pitching Moment CM:
Whereby: Cmac = 0.2996m (Mean Aerodynamic Chord) Cpivot = 0.14475m (pivot point for pitching moment) Wind Tunnel Wall Corrections
The incidence angle and the drag coefficient need to be corrected since the downstream of the wing trailing vortex system occurred due to the wind tunnel walls. The following equation rectifies any error caused during the operation of the tunnel.
;
Ɛ
αcorrected = αmeasured + ɛ;
CDcorrected = CDuncorrected + ɛ CL
Whereby: S = Wing area 2
CR = 0.9348m (Cross Section Area of the wind tunnel working section) Air Density and Viscosity
In order to determine the average free-stream velocity and Reynolds number, average air density and viscosity is required by using the following equation Patm (mmHg), T tunnel ( c)
288 Patm Kg / m 3 760 T tunnel (t )
P 1.2256
] [ ][
1.783 10
5
T tunnel (t ) Kg / ms 288
[]
Average Velocity and Reynolds Number
√ [] √ [ ] = 1071.36m/s Polhamus Leading-Edge Suction Analogy Polhamus is a simple way of estimating “Vortex lift” named after Edward C. Polhamus in 1971. The Polhamus suction analogy states that the extra normal force that is produced by a highly swept wing at high angles of attack is equal to the loss of leading edge suction associated with the separated flow. The figure below shows how, according to this idea, the leading edge suction force present in attached flow (upper figure) is transformed to a lifting force when the flow separates and forms a leading edge vortex ( lower figure).
C L K p sin cos2 KV sin 2 cos
K p KV 2
In radians
C D C Do K p sin 2 cos KV sin 3
C D K p 2 KV 3 o
Whereby: K p
dC L d
,
2C Di K i 2 C L
,
K V
( K p
2
K p K i )
c os LE
