Which are the basic components of a conventional transport aircraft configuration? What is the reason for this design, i.e. division in these components? Which main tasks are related to these components?
negative dCm/dCL and positive pitching moment at zero Lift
Sketch the characteristic curves of a lift, drag (Lilienthal) and pitching moment polar?
Which characteristics of a pitching moment polar are related to static longitudinal stability?
Which are the two primary tasks in aerodynamics? Are their solutions unique?
evaluation task: known: geometry, wanted: pressure and lift distribution, unique solution.
design task: known: target lift and pressure distribution, wanted: geometry.
Design task does not lead to an unique solution, because different geometries can lead to the same lift and pressure distribution
Consider a steady level flight. Which quantities determine the required lift coefficient?
C_L = (2*m*g) / (rho*V^2*S)
increases with area loading ((m*g) / S)
increases with flight altitude (1 / rho)
decreases quadratically with the velocity (1 / V^2)
Which components of a conventional aircraft configuration are assigned to the following essential functions, namely stability, control and high-lift?
stability: horizontal and vertical tail
control: horizontal and vertical rudders, ailerons
high lift: flaps (trailing edge) and slats (leading edge)
What is meant by center of pressure and neutral point (aerodynamic center)?
Which quantities influence the movement of the center of pressure?
In which way changes the location of the center of pressure with the decrease in flight velocity at steady level flight?
center of pressure: where all acting forces can be summed up (lift, drag) to a resultant force without any moment / Defined as the intersection point of the line of action of the resulting aerodynamic force composed of lift and drag with the airfoil chord
neutral point: where the pitching moment coeff. does not vary with a changing lift coeff. (i.e. AoA) / Defined as the intersection point of the line of action of the additional force based on a change of AoA with the airfoil chord
center of pressure is influenced by AoA, because C_L is proportional to AoA
location of center of pressure changes forward to the neutral point, because AoA increases
to fix the center of pressure we can set C_m0 to null (or to a very small number); if camber line is negative in the front and positive in the rear
Which types of movement are related to a geometrically mainly symmetric aircraft configuration? Which degrees of freedom as well as forces and moments are assigned to these types of motion? Give typical flight mechanics-related examples for these types of motion!
symmetrical, anti symmetrical and asymmetrical motions
longitudinal motion (phugoid)
forces and moment coeffs: lift, drag and pitching moment coefficients.
degrees of freedom: Ma, AoA and pitch angular velocity
lateral motion (dutch roll)
forces and moment coeffs.: yawing moment coeff., rolling moment coeff. and side force coeff.
degrees of freedom: yawing and rolling angular velocity, sideslip angle
coupled motion at anti symmetrical configs due to flow separation (spin)
forces and moment coeffs.: longitudinal force, side force, lateral force, normal force
degrees of freedom: AoA, sideslip angle, pitch-, roll- and yaw angular velocity
What is the velocity potential equation for incompressible flow (formula)? What kind of equation is it (mathematically)? Is this equation an exact solution of the Navier-Stokes-equations (for the assumptions made)?
laplace equation
under the assumption of inviscid and incompressible flow it is an exact solution
Give the definitions for Mach number and Reynolds number! Which physical effects are associated with these characteristic numbers?
Ma = free stream velocity / speed of sound, compressibility and sonic regime
Re = (free stream velocity * length) / kinematic viscosity, inertial forces vs friction force
Sketch the transition path from a trimmed flight state at lift coefficient CL1 to a higher level CL2 using a CL -Cm-diagram and explain the characteristics! In which way changes the setting angle of the stabilizer, i.e. the horizontal tail plane (consider a conventional transport aircraft configuration)?
the angle of the stabilizer decreases from CL1 to CL2
Which physical characteristics are related to a flow described by a velocity potential?
irrotational flow
inviscid flow
incompressible flow
stationary flow
Which conditions have to be fulfilled for natural static longitudinal stability?
CG is in front of the neutral point (aerodynamic center)
C_m0 is > 0
(dC_m / dC_L) < 0
C_L = n*C_W
How big is the drag coefficient relative to the zero drag coefficient at optimum glide number (symmetric polar)? Demonstrate the relationship for the Lilienthal polar!
drag coeff. at optimum glide number = 2 * zero drag coeff.
induced drag coeff. = zero drag coeff.
What is meant by the Prandtl hypothesis?
the flow around a body can be divided into two regions
a thin viscous boundary layer with velocity -> 0 at airfoil surface (rotational, viscous)
and a region with an inviscid flow outside the boundary layer (irrotational, inviscid)
-> we only have to calculate with the irrotational flow and can neglect everything happening in the boundary layer since the pressure in the outer area is nearly the same as on the surface in the boundary layer (constant in boundary layer, no pressure discontinuity between b.l. and outer domain.)
Which two conservation laws are involved in the derivation of the velocity potential equation? Which formulations appear for incompressible and inviscid flow?
mass continuity and momentum equation (energy conservation equation not required)
incompressible flow: Ma = 0=>a = sound velocity = infinite,
inviscid flow: viscosity is zero
Obtain velocity potential equation and Bernoulli equation by integrating on a streamline
What is the velocity potential for a source and a vortex in two-dimensional flow?
Source
Vortex
Which fundamental boundary condition is applied for modeling the flow around bodies on the basis of the potential theory (sketch and formula)?
kinematic boundary condition: the flow is attached/follows the contour of the airfoil. velocity vector*surface normal vector=0, vectors normal to each other.
Linearization: w/U=df/dx = contour gradient. Formula to be known.
Which potential flow modeling is associated with airfoil theory? (subproblems)
thickness problem: source distribution
lift/camber line problem: vortex distribution
Using velocity potential, Kinematic Boundary condition applied, attached flow (flow follows contourline/camberline for example)
How is the source stength determined for the symmetric airfoil problem (thickness problem)
Which resultant pressure force occurs on the symmetric airfoil at no incidence
no normal forces (no lift) due to equal pressures above and below the airfoil
no forces in free stream direction (no drag) -> d’Alembert paradox
What is the kinematic boundary condition applied to the camber line theory (small camber)
AoA and contour gradient.
u << U_infinite and dS/dx small -> neglegtable
Which quantities determine the circulation distribution for the inclined flat plane
U and AoA
Sketch the circulation and differential pressure distribution, respectively, for the inclined flat plate
Delta Cp -> infinite at root bc of root singularity
Delta Cp -> 0 at trailing edge bc of KAB
Circulation follows bc Delta Cp = (2*gamma)/U_infinite
Which flow physical characteristics are described by the flow-off condition named Kutta-Joukowski condition?
trailing edge: delta Cp = 0 and circulation is 0
Kutta summuary
For a given AoA the value of the circulation around the airfoil is such that the flow leaves the trailing edge smoothly
trailing edge angle finite -> trailing edge = stagnation point
trailing edge cusped -> velocitys at bottom and top are finite and equal in direction and magnitude
Which relations are approximately obtained for the normal and axial force on the inclined flat plate (given: rho, U_infinite, Gamma)? Which value is obtained for the lift gradient; which locations are derived from the center of pressure and the aerodynamic center (neutral point)?
normal force Fy = rho*U_infinity*Gamma
axial Force Fx = -rho*U_infinity*Gamma*AoA -> minus leads to suction force (nose thrust)
due to d’Alembert paradoxon no drag
lift coefficient gradient 2*pi
locations of center of pressure and aerodynamic center both at 1/4
Which parts of the Birnbaum-Ackermann normal distributions determine the lift coefficient and the pitching moment coefficient for an inclined cambered airfoil
Lift Coeff: A0 and A1
Pitching moment coefficient: A1 and A2
Which typical separation phenomena are in principle related to thin and thick airfoils, respecitvely? What is meant by “thin airfoil stall”
for thin airfoils separation starts at leading edge -> leading edge stall
for thick airfoils separation starts at trailing edge and progresses upstream -> trailing edge stall
thin airfoil stall = flow separates at leading edge but reattaches downstream -> separation bubble in 2D and reattachment in turbulent area
How does the airfoil thickness influence the maximum lift coefficient (reason)? Is there an optimal range?
thicker airofils lead to an increasing max. lift coeff. but if its too thick (>12%) the max lift coeff. decreases -> optimum around 12%
Also with an increase in thickness can increase radius at Leading edge causing suction
Sketch the influence on the lift polar due to a deflection of a) a trailing-edge flap, b) a leading-edge flap (slat), and c) both a leading and a trailing edge flap
trailing edge flap: affect Kutta cond., positive deflection -> increase in CL0 and CLmax
leading-edge flap: CLmax increases at higher AoA, higher Aoa possible, allows for the CLmax to be reached at higher alphas
if both are active you can superposition them
Which quantities contribute to the lift increase when deploying a Fowler flap
increasing camber -> increasing CL0 -> increasing CL
increasing surface
energisation of the top layer via through flow
Why show trailing edge flaps a higher effectivenes on the increase in zero lift coefficient compared to the effectiveness of leading edge flaps?
Flap deflection is more effective than a slat, because max. camber position is shifted dowstream and increases the zero lift coefficient.
Which potential flow modeling is applied to a wing of finite span
Horseshoe vortex model
How can the development of a wing tip vortex physically explained
difference in pressure between upper and lower side; naturally p wants to equalize: high pressure from bottom curls up
How does the wake vortex system influence the aerodynamic forces acting on a wing
Induction of tip vortices: induced downward velocity, thus reduction in effective AoA from nominal AoA
How is the lateral distance of the rolled up wake vortex system determined bsaed on the knowledge of the spanwise circulation distribution?
For elliptical lift distribution: b’ = (pi/4) b
Which modeling is related to the Prandtl lifting line theory (sketch, explanation)?
Which Ansatz is used for the circulation distribution?
system of infinitesimal horseshoe vortices whose “heads” (bound/root vortex) are placed on a common line, the lifting line
Ansatz: Fourier sine series
Which parts of the Circulation Ansatz function determine lift and induced drag
Lift: only Gamma 1
Induced Drag: Gamma n (for elliptical distribution only Gamma 1)
Which special meaning is related to the elliptical circulation distriution? Sketch the associated downwash distribution! Which relations are obtained for the induced angle of attack and the induced drag in dependence of the lift coefficient?
C_Di min, constant downwash velocity
alpha ~ CL and C_Di ~ C_L^2
In which case there is always an elliptical circulation distribution independent of the angle of attack
Elliptical wing shape, quarter line is unswept
How do aspect ratio and taper ratio influence the induced drag
AR up -> C_Di down
Lambda down -> C_Di down (not a big influence), taper ratio influences circulation distribution
Which part of the circulation Ansatz function is relevant for the rolling moment? Which dependency is on the aspect ratio?
Gamma 2 -> antimetrical; Gamma2 sin(2*theta) is antimetrical. So one side of wing has up force, other side down force -> rolling moment
Mx =
with:
Which feature characterizes the Pistolesi point
Point where downwash of the bounded vortex corresponds to the downwash according to the camber theory x= 3/4 * l
kinematic b.c. is applied there
Explain the approach of the vortex lattice method
Each lattice element corresponds to a small wing on which Prandtls theory is applied. The circulation distribution of each lattice element is concentrated on a bound vortex located at 1/4 line. Each bound vortex is continued by two trailing vortices. The circulatoin of each of those horseshoe vortices is determined based in the condition that the kinematic b.c. is fulfilled at the 3/4 point of each lattice element
Sketch the pressure distribution (qualitatively) for a symmetric airfoil with the location of maximum thickness at 30% chord and 12% relative thickness for a moderate incidence and subsonice flow. How does the pressure distribution change with an incease in AoA? At which areas a laminar respectively a turbulent boundary layer is expected (reason)? Are there areas subject to flow separation risks (reasons)? How does a shift of the location of maximum thickness to 50% chord affect the pressure distribution?
NACA 0012 (see appendix)
pressure minimum ahead of max thickness
increase of AoA: suction peak moves upstream and magnitude inreases
Transition Re<10^6 downstream of pressure minimum, Re>10^6 upstream of pressure minimum
high adverse pressure gradient -> danger of separation
Name and reason measure to reduce a suction peak on an airfoil upper side
slats to energize flow
no harsh contour gradients
thicker airfoil
Sketch delta cP for flat plate in cruise condition. What happens when you switch to climb?
(how does cP behave, draw second curve into diagram). What characteristics does curve
have?
Which 2 approaches are used within the airfoil design process (brief characterization)
direct and inverse design
direct: geometry given (calculation task), modifications to airfoil geometry to improve performance
inverse: optimization of airfoil geometry based on objective function
How can a laminar boundary layer be obtained on an airfoil for a path as long as possible? Provide a sketch of airfoil geometry and corresponding pressure distribution!
Constant flow acceleration, pressure gradient, rear placed max camber and thickness allowing a smooth acceleration and negative pressure gradient. This allows laminar flow and an indicaiton of flow separation
Glauert Integral calculation
Show the separation behaviour of an airfoil with t/c=12% which is close to stall
Sketch downwash distribution of an elliptical wing
How can the zero moment Cm0 be explained?
What is the linearized pressure coefficient cp?
Show separation behaviour of airfoil close to stall with t/c = 21% and explain what happens (prbly thick airfoil separation)
Through which effect is the end of the linear range of the pitching moment characterized?
With an increasing angle of attack, the flow starts to separate on the upper side of the airfoil - first in the rear section → ”End of the linear range”, drop in the lift!
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