JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-Requisites

Nil

Course Objectives:

• Discuss the fundamental aspects of numerical discretization and the major theories, approaches and methodologies used in computational aerodynamics.
• Analyze to build up the skills in the actual implementation of computational aerodynamics methods boundary conditions, turbulence modelling etc by using commercial CFD codes.
• Demonstrate the applications of CFD for classic fluid dynamics problems and basic thoughts and philosophy associated with CFD.
• Understand the various grids used in practice, including some recommendations related to grid quality and choose appropriate data structure to solve problems in real world.

Course Outcomes:

• Mesh creation technique
• Solving PDF by using numerical technique

UNIT - I

Introduction to Computational Aerodynamics: Need of computational fluid dynamics, philosophy of CFD, CFD as a research tool as a design tool, applications in various branches of engineering, models of fluid flow finite control volume, infinitesimal fluid element, substantial derivative physical meaning of divergence of velocity, derivation of continuity, momentum and energy equations, physical boundary conditions significance of conservation and non-conservation forms and their implication on CFD applications strong and weak conservation forms shock capturing and shock fitting approaches.

UNIT - II

Mathematical Behavior of Partial Differential Equations and Their Impact On Computational Aerodynamics: Classification of quasi-linear partial differential equations by Cramer‘s rule and Eigen value method, general behavior of different classes of partial differential equations and their importance in understanding physical and CFD aspects of aerodynamic problems at different Mach numbers involving hyperbolic, parabolic and elliptic equations: domain of dependence and range of influence for hyperbolic equations, well-posed problems.

UNIT - III

Basic Aspects of Discretization: Introduction to finite difference: finite difference approximation for first order, second order and mixed derivatives, explicit and implicit approaches, truncation and round- off errors, consistency, stability, accuracy, convergence, efficiency of numerical solutions. Von Neumann stability analysis, physical significance of CFL stability condition. Need for grid generation, structured grids artesian grids, stretched (compressed) grids, body fitted structured grids, H-mesh, C- mesh, O-mesh, I-mesh, multi-block grids, C-H mesh, H-O-H mesh, overset grids, adaptive grids, unstructured grids: triangular, tetrahedral cells, hybrid grids, quadrilateral, hexahedral cells.

UNIT - IV

CFD Techniques: Lax-Wendroff technique, MacCormack‘s technique, Crank Nicholson technique, Relaxation technique, aspects of numerical dissipation and dispersion. Alternating-Direction-Implicit (ADI) Technique, pressure correction technique: application to incompressible viscous flow, need for staggered grid. Philosophy of pressure correction method, pressure correction formula. Numerical procedures: SIMPLE, SIMPLER, SIMPLEC and PISO algorithms, boundary conditions for the pressure correction method.

R18 B.TECH AERONAUTICAL ENGG. III YEAR

UNIT - V

Finite Volume Methods: Basis of finite volume method, conditions on the finite volume selections, cell-centered and cell vertex approaches. Definition of finite volume discretization, general formulation of a numerical scheme, two-dimensional finite volume method with example.

TEXT BOOKS:

• 1. J. D. Anderson, Jr., ―Computational Fluid Dynamics- The Basics with Applicationsǁ, McGraw-Hill Inc, 2012.
• 2. D. A. Anderson, J. C. Tannehill, R. H. Pletcher, ―Computational Fluid Mechanics and Heat Transferǁ, 1st edition, 1997.

REFERENCE BOOKS:

• 1. Hirsch, C., ―Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamicsǁ, Vol. I, Butter worth-Heinemann, 2nd edition, 2007.
• 2. Hoffmann, K. A. and Chiang, S. T., ―Computational Fluid Dynamics for Engineersǁ, Engineering Education Systems, 4th edition, 2000.
• 3. Patankar, S.V., ―Numerical Heat Transfer and Fluid Flowǁ, Hemisphere Pub. Corporation, 1st edition, 1980. R18 B.TECH AERONAUTICAL ENGG. III YEAR