ME666A |
Inviscid Flows |
Credits: |
3-0-0-9 |
Course Content:
Vorticity, vorticity equation, Kelvin’s theorem, Helmholtz laws, kinematic decomposition of velocity fields, uniqueness of solenoidal and irrotational velocity fields, superposition of irrotational flows, complex analysis, conformal transformations, finite wings, three-dimensional potential flows, unsteady potential flows, virtual mass, cavitation, bubble dynamics, interfacial and free-surface waves, bores and hydraulic jumps.
No. of Lectures (40 Lectures)
I. Introduction(1 lecture):
- Continuity equation, Navier-Stokes equations, Bernoulli equation
II. Vorticity dynamics (12 Lectures):
- Vorticity, vortex lines and tubes, vorticity equation, circulation, Kelvin’s circulation theorem, Helmholtz laws, creation of vorticity, Helmholtz’s kinematic decomposition, Biot-Savart law, inviscid motion of point vortices, line and sheet vortices, image vorticity, vortex momentum, uniqueness of solenoidal and irrotational velocity fields in singly- and multiply-connected domains, Kelvin’s minimum energy theorem, superposition of irrotational flows
III. Potential flows (17 Lectures):
- Stream function and velocity potential, complex analysis, standard flow patterns, circle theorem, Blasius integral laws, conformal transformations, Jowkowski transformation, introduction to thin-airfoil theory, finite wings, introduction to lifting-line theory, Schwarz-Christoffel theorem, axisymmetric and three-dimensional potential flows, sphere theorem, nature of 3D far-fields, unsteady potential flows, virtual mass
IV. Elements of bubble dynamics (3 Lectures):
- Rayleigh equation, Rayleigh-Plesset equation, cavitation and bubble collapse
V. Interfacial waves and free-surface flows (7 Lectures):
- Small amplitude waves at free surfaces and interfaces, non-linear theory of shallow-water waves, method of characteristics, bores and hydraulic jumps
Target audience:
- PG and 3rd, 4th year UG students
Suggested Readings:
- Milne-Thomson, L. M. “Theoretical Hydrodynamics”, 5th Ed., Dover
- Milne-Thomson, L. M. “Theoretical Aerodynamics”, 4th Ed., Dover
- Vallentine, H. R. “Applied Hydrodynamics”, 2nd Ed., Butterworths
- Batchelor, G. K. “Introduction to Fluid Dynamics”, 1st Indian Ed., Foundation Books
- Panton, R. L. “Incompressible Flow”, 3rd Ed., Wiley
- Lighthill, J. “An Informal Introduction to Theoretical Fluid Mechanics”, Oxford Clarendon
- Currie, I. G. “Fundamental Mechanics of Fluids”, 4th Ed., CRC Press