MAE 5130: VISCOUS FLOWS Lecture 1: Introduction and Overview August 17, 2010 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

COURSE OVERVIEW Study of Viscous Flows → Flows of Engineering and Scientific Interest Review of fluid mechanics, properties, vector calculus, kinematics, thermodynamics, and heat transfer (4-5 lectures) Derivation of governing equations of motion for fluid flows (5-6 lectures) Navier-Stokes equations in full glory Differential form Integral (control volume) form Gain physical insight into what various terms in equations represent Supplemented with examples and non-dimensionalization Common (analytical) solutions to N-S equations (~ 10 lectures) Examples and applications Note that N-S equations are fundamental and rigorous, but non-linear, non-unique, complex and difficult to solve (does a solution even exist?) Boundary layers (important even in flows with low viscosity) (~10 lectures) Laminar Stability and transition Turbulent (also turbulent bulk mean flow) Application and examples of engineering interest

NAVIER-STOKES EQUATIONS

EXAMPLES OF EXTERNAL AND INTERNAL B.L.

EXAMPLE: VORTICITY ARUND A BEND Baroclinic Torque Case 1 Case 2

EXAMPLE: VORTICITY AROUND A STRUT

EXAMPLE: VORTICITY AROUND A STRUT

EXAMPLE: VARIABLE DENSITY CONTRACTION

EXAMPLE: SHOCK ENHANCED MIXING

STREAMLINE AND STREAM FUNCTION EXAMPLE y=0 y=1 y=2 f=0 f=1 f=2