Aero 316 Flashcards
Viscous flow
Viscous effects are accounted for; real flow.
Inviscid flow
Approximated flow without viscous effects. No friction, diffusion or thermal conduction. The Reynolds number tends to infinity.
Reynolds number definition
Ratio of inertial to viscous forces.
Reynolds number equation
Re = (RhoVL)/µ
Incompressible flow
Flow with constant density
Compressible flow
Flow with variable density
Euler frame of reference
Finite control volume fixed in space with the fluid moving through it.
Lagrangian frame of reference
Finite control volume moving with the fluid such that the fluid particles stay the same within the control volume.
Divergence of a vector field
Tells us for each point in space how much more flows into the vicinity of that point than out of it. Thus, the divergence indicates if there are sources or sinks.
Gradient of a scalar field
Nabla * Phi = grad(phi)
Divergence of a vector field, div(V)
Nabla dot V
Curl of a vector field
Nabla cross V = curl(V)
Vorticity
The curl of a velocity field, Nabla cross V. It’s also twice the angular velocity.
Irrotational flow
Vorticity is zero everywhere in the flow. Fluid elements have no angular velocity, and motion is pure translation.
Condition of irrotational flow
A scalar function, phi, can be introduced such that Nabla * phi = V, since Nabla cross Nabla*phi = 0.
Potential flow theory
Describes flow with a single, linear partial differential equation.
Governing equation of potential flow theory
Laplace equation.
Streamline
A line which is tangential to the local velocity vector everywhere along its length.
Stream function
Constant value along a streamline.
What does the velocity potential function automatically satisfy?
The condition of irrotationality.
What does the stream function automatically satisfy?
The condition of mass conservation.
Four elementary solutions that satisfy the Laplace equation
Uniform flow, Source/sink flow, Doublet flow and Potential vortex flow.
Property of doublet flow
No net mass production/destruction, therefore a closed flow field is created.
How could you approximate the flow over a circular cylinder?
Superimpose doublet flow with uniform flow.
Circulation of flow
A contour integral of the tangential velocity along a closed curve.
Potential vortex
Flow shows a rotational motion around the origin, with the streamlines describing concentric circles centred on the origin.
Critical mach number
The free-stream mach number at which a local mach number of 1.0 is first obtained somewhere within the flow.
Drag divergence mach number
Value of the mach number where a sudden increase in drag is observed, increasing by a factor of ten or more.
Assumptions to derive thin aerofoil theory
Inviscid, irrotational and incompressible flow.
Origin of vortex flow
Singularity where the curl of the velocity is infinite.
Kinematic flow condition of thin aerofoil theory
There must be no normal velocity component to the camber line.
Continuum flow
Mean-free path of molecules is order of magnitude smaller than scale of body.
Low-density and free molecule flow
Mean-free path of molecules is of same order as scale of body. It is necessary to account for the molecular motion.
Inviscid flow
Approximated flow without viscous effects. No friction, thermal conduction or diffusion. Reynolds number tends to infinity.
tauxy
µ*(du/dy), where µ is the viscosity coefficient and du/dy is the velocity gradient.
q dot
-k*(dT/dy), where k is the thermal conductivity, and dT/dy is the temperature gradient.
Source strength of source/sink flow, ^
^ = 2πrVr, where Vr is the radial velocity.
Kutta-Joukowski Theorem
L’ = Rho∞V∞gamma
d’Alembert’s Paradox
D’ = 0
When can boundary layers be defined?
When viscous effects mostly occur in relatively thin layers along solid walls. Outside of these layers, viscous effects are secondary or even negligible.
Four key features of a boundary layer
- Velocity along the wall changes rapidly with increasing distance from the wall.
- Strong gradients occur in the wall normal direction.
- Close to the wall, the velocity is substantially lower than outside the boundary layer.
- No-slip condition.
No-slip condition
Fluid velocity is zero relative to the wall at the wall.
Where is the edge of a boundary layer usually defined?
The point where the velocity reaches 99% of the free-stream velocity.
Displacement thickness
The thickness of the region carrying the ‘lost’ mass-flow rate at the free-stream velocity.
Momentum thickness
The reduced velocity close to the wall in a boundary layer corresponds to a loss in momentum compared to the undisturbed free-stream velocity.
Shape factor
Relates the displacement thickness and the momentum thickness as H=∂/theta, where ∂ is the displacement thickness and theta is the momentum thickness.
Viscous flow around a cylinder - low Reynolds number
Flow stays attached and is almost completely symmetrical. Viscous effects dominate the linear inertial effects.
Viscous flow around a cylinder - high Reynolds number
Extent of flow separation and type of flow field created is equally dependant on viscous and inertial effects.
Negative pressure gradient in direction of mean flow
Beneficial to the stability of the boundary layer.
Positive pressure gradient in the direction of the mean flow
Detrimental to the stability of the boundary layer, resulting in decelerating flow. Velocity might approach zero, leading to separation.
What does turbulence enhance?
The mixing of momentum in the boundary layer.
Where are compressibility effects considered?
For M>0.3
In the NACA 4-digit series, what do m and p represent?
m is the maximum camber of the aerofoil, and p is the location of the maximum camber. m is the first number, and p is the second number.
What does alpha0 not depend on?
The aspect ratio.
Kutta condition definition
A body with a sharp trailing edge which is moving through a fluid will create about itself a circulation of sufficient strength to hold the rear stagnation point at the trailing edge.
Cl max in thin aerofoil theory
There’s no Clmax since flow is inviscid.
Drag in thin aerofoil theory
D’Alembert’s paradox states there is no drag for potential flow.
What are the contributions to the drag coefficient, CD?
The profile drag, cd, which is mostly friction force, and the induced drag, which is due to wing tip vortices.
How to prove mass conservation
∂u/∂x + ∂v/∂y = 0
How to prove irrotationality
∂u/∂y - ∂v/∂x = 0
Why can linear combinations of the solution to the Laplace equation be used to describe more complex flow fields?
Because superposition is possible since the Laplace equation is linear.
When flow is turned into itself (concave corner), what type of shock forms?
Oblique shock
When flow is turned away from itself, what occurs?
An expansion wave
Mach angle equation
sinµ = 1/M
How are the Euler equations obtained?
By removing the viscous and heat conduction effects from the Navier-Stokes equations.
Velocity components for potential vortex flow
Vr = 0, Vtheta = K/r, where K is the strength of the vortex.
Circulation for potential vortex
Gamma = -2πK, where K is the strength of the vortex.
Two assumptions when deriving the boundary layer equations.
The Reynolds number is very large, 1/Re = O∂^2, and the boundary layer is very thin, ∂ «_space;c.
State the mathematical character of Blasius’ boundary layer equation
Single, third-order, non-linear ODE.
Units of circulation
m^2/s
Two real world concepts pursued in the aviation sector to design future wings.
- Natural or hybrid laminar flow control. Causes drag reduction from lower skin friction. Slope of laminar profile is lower.
- Hinged wing tips, to increase aspect ratio, resulting in reduced induced drag.
