Concise - All Theory Flashcards
As an arbitrary camber line shape can be specified in thin aerofoil theory, the effect of flaps and slats can be assessed. Why is this problematic theoretically?
- Thin Aerofoil theory requires a continuous camber line
- Flaps and slats usually have a small gap
- Theory cannot predict stall
- Gap delays stall significantly
What are the limitations of the aerofoil geometry obtained with the Joukowski transformation?
- Fixed thickness distribution; maximum thickness at c/4
- Camber line is a circular arc; maximum camber at midpoint
- Trailing edge is cusped and not physically realizable
What are the key limitations of predictions of aerofoil performance obtained from either Juokowski or Thin Aerofoil analysis?
- Assumes inviscid flow
- Drag is predicted as zero
- Cannot predict stall and separation
What are the key limitations of the predictions from thin aerofoil theory?
- Predicts constant pitching moment about 1/4 chord (aerodynamic center)
- Thickness moves aerodynamic center forward
- Pressure distribution disagrees with experiments near leading/trailing edge
- Aerofoil coefficients are reliable
- Drag predicted as zero
What is the Kutta condition?
- Empirical rule based on trailing edge flow
- Flow leaves sharp trailing edge smoothly with finite velocity
- Consequences:
- Velocities at trailing edge (upper & lower) are identical
- Pressure difference between surfaces vanishes at trailing edge
In general, will an aerofoil generate the circulation, and hence lift, indicated by the analysis of the Joukowski aerofoil? Explain why
- No circulation/lift as per Joukowski analysis
- Reasons:
- Real fluid is viscous; boundary layer and wake affect flow
- Physical trailing edge is rounded; separation point deviates from theoretical Kutta condition
Explain why the Kutta condition is needed to analysis a Joukowski aerofoil
- Avoids infinite velocity at trailing edge
- Determines appropriate circulation for lift
- Provides additional constraint for streamline flow around aerofoil
Explain how a flap with a gap between it and the main aerofoil helps to delay the onset of stall.
- Gap allows high pressure, high momentum fluid to leak into boundary layer
- Reduces momentum deficit in boundary layer
- Avoids boundary layer separation (stall)
Why was an elliptic planform for a wing considered to be advantageous?
- Elliptic spanwise lift distribution yields minimum induced drag
- Requires elliptic spanwise chord variation without geometric/aerodynamic twist
- Achieves minimum induced drag
What is geometric twist in the context of a finite wing and explain the benefit and challenge it represents.
- Geometric twist: angle of attack/chordline varies with spanwise position
- Purpose: achieve spanwise lift distribution to minimize induced drag (e.g., elliptic circulation)
- Challenge: constructing twisted structures is difficult with metal airframes
Explain why birds flying in a V-formation is advantageous.
- V-formation allows trailing tip vortices from adjacent birds to overlap
- Counter-rotating vortices cancel each other
- Reduces downwash effect, leading to less induced drag and lower power requirements
- Leading bird experiences downwash; trailing positions experience upwash
- Not all positions in the V formation receive equal benefits
State Helmholz’s third theorem that governs vortex filaments and explain the consequence for flow around a wing of finite span.
- Helmholtz’s Third Theorem:
- In absence of external rotational forces, initially irrotational fluid remains irrotational
- Circulation around fluid particles initially zero remains zero
- Consequence for finite wings:
- To generate lift (non-zero circulation), an opposite circulation (starting vortex) must be shed from the trailing edge
- Starting vortex convects downstream and its effect diminishes over time, negligible in steady conditions
What are the limitations of the Prandtl lifting line theory for 3D wings (i.e. stacked horse vortices)?
- Does not account for viscous flow or swept wings
- Assumes shed vorticity sheet remains planar
- Limitations:
- Vorticity sheet actually rolls into single wing tip vortices
- Wing tip vortices induce downward velocity in each other, causing trailing vortices to be below the wing
- Trailing vortices are not in the same plane
How are Helmholtz’ theorems for the motion of vortex filaments satisfied for a 2D aerfoil?
- 2D vortex filament slice is a point vortex
- Vortex filaments are parallel to the z-axis in 2D flow
- Helmholtz’s First and Second Theorems:
- Constant strength filaments
- Filaments extend to +/- infinity
- Third Theorem:
- No removal or change in vortex strength over time
- Satisfied in inviscid flow
State Helmhotz’s first two theorems governing vortex filaments and explain the consequence for flow around a wing of finite span.
- Helmholtz’s First Two Theorems:
- Vortex filament strength is constant along its entire length
- Vortex filament cannot end in fluid; must extend to boundaries or form closed loops
- Consequence:
- Lifting wings generate wing tip vortices extending downstream towards infinity
What is aerodynamic twist in the context of a finite span wing and explain the purpose of this feature.
- Aerodynamic twist: shape (camber) of aerofoil varies with spanwise position
- Purpose:
- Achieve spanwise lift distribution to minimize induced drag (e.g., elliptic circulation)
- Help avoid stall on specific parts of the wing
What are the characteristics of turbulent buffeting as a flow-induced vibration mechanism?
- Broadband, low amplitude random excitation
- Amplitude proportional to flow velocity
- Excitation independent of structural response (no fluid-structure feedback)
- Can be studied with rigid models (forced response)
- Cannot be fully eliminated; managed with extra damping
What are the characteristics of "fluid stiffness" in the context of flow induced vibration?
- Fluid stiffness: fluid force in phase with structure displacement
- Requires only structural deformation, no vibration
- Measurable with rigid, statically displaced models
In the context of flow induced vibration, what is meant by dynamic stability.
- Dynamic stability: small perturbations lead to oscillations with decreasing amplitude
- May involve negative fluid stiffness and higher structural damping
- Net system damping remains positive
What are the characteristics of fluidelastic instability (or aero- or hydro-elastic instability) as a flow-induced vibration mechanism?
- Self-excited structural response; fluid force depends on structural displacement/motion
- Strong feedback path; fluid and structural systems are coupled
- Complex models and testing; must match fluid and structural parameters (damping ratio, natural frequency)
- Onset prediction requires semi-empirical or linearized models
- Limited by non-linear behavior or potential for total failure
In the context of flow induced vibration, what is meant by static divergence or static instability.
- Static divergence: small perturbations cause structural deflection to increase monotonically over time
- Caused by net negative stiffness (positive structural stiffness < negative fluid stiffness)
- Example: torsional divergence of aircraft wings (e.g., Gruman X29)
What are the characteristics of "fluid damping" in the context of flow induced vibration?
- Fluid damping: fluid force out of phase with structure displacement
- Time delays (vorticity transport) or relative velocity changes can cause negative damping
- Negative damping can lead to dynamic instability
What are the characteristics of periodic vortex shedding as a flow-induced vibration mechanism?
- Narrow band, nearly sinusoidal excitation; frequency proportional to flow velocity (Strouhal number)
- Problematic when vortex shedding frequency matches structure’s natural frequency
- Weak feedback causes vortex shedding to lock-on to natural frequency near coincidence
- Response remains a forced response
- Susceptibility can be assessed using rigid models; structural motion not required
In the context of flow induced vibration, what is meant by dynamic instability.
- Dynamic instability: small perturbations lead to vibrations with increasing amplitude
- Caused by negative net damping in at least one vibration mode
- Examples: galloping, classical flutter in single degree of freedom systems
What is meant by stall for an aerofoil? How does it affect the performance of the aerofoil?
- Stall occurs when the angle of attack increases
- Causes boundary layer separation from the upper surface
- Results in reduction of lift
- Leads to a dramatic increase in drag
Define the angle of attack of an aerfoil. Describe what orientation the aerofoil would be in at a positive angle of attack.
- Angle of attack is the angle between the freestream velocity direction and the chordline
- At a positive angle of attack, the leading edge is up (above the trailing edge)
Specify what the conditions (in terms of non-dimensional quantities) are necessary for an assumption of incompressibility in the flow to be valid.
- Incompressibility conditions:
- Mach number squared (M²) much less than 1
- (M/Fr)² much less than 1
- M²/Re much less than 1
- Where:
- M = Mach number
- Fr = Froude number
- Re = Reynolds number
Define the aerodynamic center.
- The aerodynamic center is the point where the pitching moment (Cm) remains constant regardless of the angle of attack
- This is valid below the stall angle
Define the Center of Pressure on an aerfoil.
- The center of pressure is the point where the pitching moment is zero
- The pressure distribution over the aerofoil can be reduced to Lift and Drag at this point
What is the camber (or camber height) of an aerofoil?
- Camber (Camber height) is the maximum deviation of the camber line from the chordline
- It measures the curvature of the aerofoil
Practically, what is the maximum allowable Mach number for the incompressible assumption to be valid?
- The maximum allowable Mach number for the incompressible flow assumption is Ma = 0.3
Compare and contrast the stream function and the velocity potential.
- Stream Function
- Defined only for 2D flows
- Represents mass continuity
- Applicable to rotational flows
- Velocity Potential
- Defined for 3D flows
- Represents irrotationality
- Does not exist for rotational flows
- Both
- When both exist, they are orthogonal
What is the significance of the curl of the velocity field in an incompressible flow?
- The curl of the velocity field is called vorticity
- Vorticity is twice the angular momentum
What is D’Alembert’s paradox? State what is the implication for 2D aerofoil theory based on potential flow.
- D’Alembert’s Paradox
- Potential flow analysis predicts zero drag
- Viscosity is neglected, so no skin friction or boundary layer separation
- Implications for 2D Aerofoil Theory
- Cannot predict drag
- Cannot predict the onset of stall
What is the Kutta-Joukowski theorem?
- Kutta-Joukowski Theorem
- Lift per unit length (L’) is proportional to circulation (Γ)
- Formula: L’ = ρUΓ
In a real fluid flow (i.e. with non-zero viscosity), where is vorticity generated and destroyed?
- Vorticity Generation
- Created by shear forces in the boundary layer
- Vorticity Destruction
- Diffused and dissipated by viscosity as it convects downstream
Define a streamline, clearly stating the key characteristics.
- Streamline
- A curve tangential to the local instantaneous velocity at every point
- No normal velocity across a streamline
- Solid bodies are streamlines in a body-fixed frame
- In steady flows, streamlines coincide with pathlines and streaklines
