Self Test 3 - Potential Flow Theory Flashcards
Compare and contrast the stream function and the velocity potential.
Velocity potential is defined for 3D flows, but the stream function only exists for 2D.
Stream function is a statement of mass continuity and so can be applied to rotational flows.
The velocity potential is a statement of irrotationality and so does not exist for rotational flows.
The stream function and velocity potential, when they both exist, are orthogonal.
What is the significance of the curl of the velocity field in an incompressible flow?
The curl is called the vorticity and it is twice the angular momentum.
What is D’Alembert’s paradox? State what the is implication for 2D aerofoil theory based on potential flow.
D’Alembert’s paradox is the observation that potential flow anaylsis can yield a good approximation of the velocity field is some circumstances, but because visosity is neglected, the predicted Drag will always be zero. The absence of viscosity means that there can be no prediction of skin friction nor of boundary layer separation. As a result, classical hydrodynamics predict zero Drag for an aerofoil and cannot predict the onset of stall.
What is the Kutta-Joukowski theorem?
Kutta and Joukowski stated that for any cross section the Lift per unit length is proportional to the circulation enclosed by a closed curve completely enveloping the section.
L’=ρUΓ
In a real fluid flow (i.e. with non-zero viscosity), where is vorticity generated and destroyed?
In general, vorticity is generated by shear forces, and so will be created in the boundary layer. As it convects downstream, vorticity will be diffused and dissipated by the action of viscosity.
Define a streamline, clearly stating the key characteristics.
A streamline is a curve which is tangential to the local instantaneous velocity at every point along its length.
The, as there is no normal velocity across a streamline, all solid bodies are streamlines in a body fixed frame of reference.
For steady flows in a body fixed frame of reference, streamlines are coincident with pathlines and streaklines.
