JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-Requisites

CFD

Course Objectives:

• Explain the concept of panel methods, analyze various boundary conditions applied and demonstrate several searching and sorting algorithms.
• Describe the initial methods applied in the process of CFD tools development their advantages and disadvantages over modern developed methods.
• Demonstrate different methods evolved in analyzing numerical stability of solutions and evaluate the parameters over which the stability depends and their range of values.
• Understand advanced techniques and methods in time marching steps and identify different boundary conditions for different cases in CFD techniques.

Course Outcomes:

• Different techniques to solve the complex fluid dynamics problem numerically

UNIT - I

Numerical Solutions: Euler equations: Flux approach, Lax-Wendroff method, basic principles of upwind schemes, flux vector splitting, Steger Warming flux vector splitting, Van Leer flux vector splitting, Upwind reconstruction, evolution, Godunov‘s first order upwind method, Roe‘s first order upwind method.

UNIT - II

Time Dependent Methods: Stability of solution, explicit methods, FTFS, FTCS, FTBS, Leapfrog method, Lax method. Implicit methods: Euler‘s FTCS, Crank Nicolson method, description of Lax- Wendroff scheme, McCormack two step predictor-corrector method, description of time split methods, approximate factorization schemes.

UNIT - III

Boundary Conditions: Boundary Layer Equations: Setting up the boundary layer equations, flat plate boundary layer solution, boundary layer transformations, explicit and implicit discretization, solution of the implicit difference equations, integration of the continuity equation, boundary layer edge and wall shear stress, Keller-box scheme. Concept of dummy cells, solid wall inviscid flow, viscous flow, farfield concept of characteristic variables, modifications for lifting bodies inlet outlet boundary, injection boundary, symmetry plane, coordinate cut, periodic boundaries, interface between grid blocks, flow gradients at boundaries of unstructured grids.

UNIT - IV

Method of Characteristics: Philosophy of method of characteristics, determination of characteristic lines, two dimensional irrotational flow, determination of compatibility equations, unit processes, supersonic nozzle design by the method of characteristics, supersonic wind tunnel nozzle, minimum length nozzles, domain of dependence and range of influence.

UNIT - V

Panel Methods: Basic formulation, boundary conditions, physical considerations, reduction of a problem to a set of linear algebraic equations, aerodynamic loads, preliminary considerations prior to establishing numerical solution, steps toward constructing a numerical solution, solution of thin airfoil with lumped vortex filament, accounting for effects of compressibility and viscosity.

TEXT BOOKS:

• 1. Tannehill John C, Anderson Dale A, Pletcher Richard H, ―Computational Fluid Mechanics and Heat Transferǁ, Taylor & Francis, 2nd Edition, 1997.
• 2. Chung T G, ―Computational Fluid Dynamicsǁ, Cambridge University Press, 2nd Edition, 2010.
• 3. Katz Joseph and Plotkin Allen, ―Low-Speed Aerodynamicsǁ, Cambridge University Press, 2nd Edition, 2006.

REFERENCE BOOKS:

• 1. Anderson J D, ―Modern Compressible Fluid Flowǁ, 2nd Edition, McGraw Hill, 1990.
• 2. Anderson J D, ―Fundamentals of Aerodynamicsǁ, Tata McGraw Hill, 5th Edition, 2010.
• 3. Anderson J D, ―Computational Fluid Dynamicsǁ, McGraw Hill, 1995.