Electives at Department of Aerospace Engineering
## List of Electives## Syllabus
Introductory Kinetic theory (definition of pressure and temperature from microscopic viewpoint, mean free path, transport processes). Equilibrium kinetic theory (Maxwell's distribution, collusion rate). Chemical equilibrium )Effective collision rate, Law of mass action, activation energy). Chemical thermodynamics (Gibb's relations, Mixture of perfect gases, van't Hoff's relation). Statistical thermodynamics (Macroscopic and microscopic descriptions, Quantum energy states, energy modes of molecules, Boltzman's relation, contribution of internal structure). Equilibrium gas properties (Ideally dissociating gas, Ionisation equilibrium, Collision cross sections). Flow with translational non-equilibrium (Bhatnagar-Gross-Krook model for translational non-equilibrium, Chapman-Enskog solution, Transport properties as nonequilibrium phonomena, Linearised Couette flow). _______________________________________________________________________________Top
An overview of object programming (OOP). Introduction to C++. Essentials of OOP - data encapsulation, overloading, inheritance. User defined data Types. Input/output. Code reusability. Templates - use of templates to write reusable code. OOP applications to numerical analysis - find epsilon of the machine, interval analysis and interval class. A matrix class. Solutions to differential equations - ODEs and PDEs using grid point class, finite volume class and finite element class. Simple graphics and visualisation. Random number generators, Monte-Carlo methods, Random walk, discrete event simulation. Object oriented design and its implications to problem formulation and solution. _______________________________________________________________________________Top
Prandtl's approximation of Navier-Stokes equations. Blasius solution for a flat plate. Integral momentum equation. Karman - Polhausen method. Walz-method. Unsteady boundary layer. Introduction to thermal and turbulent boundary layers. _______________________________________________________________________________Top
Introduction to computation methods. Examples : Method of steepest descent, numerical integration, interpolation, etc. Relaxation methods applied to subsonic and transonic flows. Method of singularities; Vortex lattice methods. Variational methods. Time-dependent methods. Treatment of shocks. Introduction to boundary-layer calculations. Introduction to finite-element method and its applications to fluid flows. _______________________________________________________________________________Top
Optimization of airplane performance : Instantaneous and integral performance problems and conditions for their optima. Optimization of range and climb performance; Energy height method. Longitudinal and lateral dynamic stability. Response of airplane to deflection of controls, gust and turbulence. Stability with automatic control. Role of analogue computers and simulators in stability analysis. Stability and control after stall. Recent trends. _______________________________________________________________________________Top
Some concepts and properties of transonic flow. Fundamental equations, similarity rule, flow in the throat of convergent-divergent nozzle, consideration of shock on an aerofoil. Methods of transonic flow calculations: Guderley profile, exact solutions by hodograph theory, parabolic method, integral method, method of Murman and Cole. Equivalence theorem and area rule. _______________________________________________________________________________Top
Thin and thick aerofoils in incompressible flow. Limitations of lifting line theory, concepts of extended lifting line theory, Lifting surface theory. Interaction problems. Small perturbation equations in compressible flows: Pradtl-Glauert and Goethert rules. Ackeret's supersonic airfoil theory. Wings of finite span in incompressible and compressible flows. Aerodynamics of the fuselage and wing-fuselage combination. _______________________________________________________________________________Top
Introduction. Rotor aerodynamics : Momentum theory for vertical and forward flight, ground effect. Rotor mechanics: Blade motion, pitch, flap and lead-lag. Performance: Hover ceilings, steady vertical and level flight, climb, range, endurance, autorotation. _______________________________________________________________________________Top
Basic definitions. Airspeed, altitude and temperature measuring systems, erros and calibration. Measurement of power of internal combustion engines, determination of corrected power. Measurement/estimation of thrust of Turboject engines. Useful thrust and s.h.p. of turboprop. Data acquisition systems. Flight test techniques for evaluation of performance and stability of aircraft with piston and jet engines. Performance reduction methods. Reduction of take-off and landing performance. _______________________________________________________________________________Top
General Introduction. The Gudonov scheme. BVLR method. Method of characteristics in two- and three-dimensional flows. Method of integral relations Blunt body problem. Particle in cell method. _______________________________________________________________________________Top
An introduction to vortex flows - vortices in everyday life - vortices in tea cup, the tornado, vortex rings. Geometrical and Kinematical preliminaries. Laws of vortex motion. Stretching, viscous diffusion and creation of vorticity. Vortex momentum. Dynamics of Vortex filaments. Dynamics of point vortices in two dimensions - The Karman Vortex street. Evolution and roll up of open and closed vortex sheets. Birkhoff-Rott equation. Kelvin-Helmholtz instability. Kaden's spiral. Dynamics of vortex patches. Controur dynamics. Starting vortex behind an airfoil. Formation of vortex rings. Structure of the trailing vortex behind the wing and vortex breakdown. Computation of vortex merging and roll-up using the vortex blob method. Computation of incompressible, unsteady flows using the random vortex method. Fast vortex methods. Introduction to computation of 3 dimensional vortex flows. _______________________________________________________________________________Top
An introduction to tensor calculus, Transformation of coordinates, General principles of grid generation, structured grids in two and three dimensions: Algebraic grid generation. Differential equation based grid generation: Elliptic, Parabolic, Hyperbolic grid generation. Cartesian grids, Unstructured Grid generation - various algorithms. Grid clustering, Grid refinement, Adaptive grids, Moving grids algorithms, CAD interface to grid generators, Techniques for complex and or large problems: Multi block methods, grid generation for distributed problem solving. _______________________________________________________________________________Top
Introduction to numerical methods - machine epsilon, numerical differentiation and integration. Advection and diffusion by wave equation, heat equation and Laplace equation. Properties of the solutions. Discretization schemes for the one dimensional first order wave equation. Dissipation, Dispersion and stability of such schemes. Simple extension to Quasi-One-Dimensional Euler equations and Full Euler equations. Solution to heat equation. Time marching schemes-ADI, LU approximate factorization schemes. Solution to Laplace equation-Point interactive technique. Properties of the solution. Introduction to grid generation-algebraic grids, elliptic grids. Applications to flow problems. _______________________________________________________________________________Top
Introduction to steady flows, their stability and bifurcations. Kelvin-Helmholtz instability. Stability of Parallel Shear Flows. Orr-Sommerfeld Problem. Temporal Stability of Parallel Shear Flows. Non-linear Stability. Stability of Boundary Layer Flows. Transition. Chaos and Turbulence. _______________________________________________________________________________Top
Introduction to linear instability and transition. Recent developments in instability methods; transient growths, global analysis, optimization and feedback mechanisms. Routes to turbulence, factors affecting different mechanisms and re-laminarization. Methods to achieve transition delay, lift augmentation, separation prevention, turbulence suppression, noise abatement and other flow control strategies. Transition control: wall heating and cooling, wall motion, suction and blowing etc. Separation control: velocity profile modifiers, shaping, heat transfer, turbulators, etc. Drag reduction: reduction of near-wall momentum, Toms effect, etc. Recent developments in flow control. _______________________________________________________________________________Top
Airfoils and wings in steady motion. Analytical methods for the unsteady aerodynamic behavior of oscilating airfoils and wings. 2D unsteady thin airfoil theory. 3D unsteady wing theory. Airfoils and wings undergoing arbitrary motion. Gust. Time domain and frequency domain analysis of unsteady flows. Kelvin impulse and apparent mass concept in unsteady flows. Aerodynamics of flapping and hovering bio-mimetic flights. Numerical techniques for unsteady potential flows. Unsteady flow-field of natural invertebrates and aquatic animals and flapping-type MAVs. Discussion on 3D and Re effects. _______________________________________________________________________________Top
Frequency domain and state space technique; control law design using Nyquist diagrams and Bode plots; state feedback, state estimation, design of dynamic control laws; elementary analysis of non-linearities and their impact on control design, basic applications of control theory to aerospace systems, navigation, guidance. _______________________________________________________________________________Top
Chemical rocket performance: Thermochemical calculations. Liquid propellant rockets: Droplet combustion, feed system and ignition, injector design, combustion chamber geometry and cooling, nozzle design, thrust vector control. Solid propellant rockets: Combustion mechanisms, grain design, two phase flow, case fabrication problems. Combustion instability. _______________________________________________________________________________Top
Introduction to aircraft gas turbines. Non-rotating components: Aero-thermodynamics of inlets, combustors and nozzles. Rotating components: Exchange of energy between rotor and fluid. Euler equation, stage performance analysis. Multistage compressors and turbines. Centrifugal and axial compressors and axial turbines. Stall and surge problems of compressors. Structural and cooling problems of turbine blades. _______________________________________________________________________________Top
Typical engine performance. Non-dimensional representation. Off
design performance estimation of turbojets. Components characteristics
and component matching: Equilibrium operation. Principles of controls
and instruments.
Review of reaction kinetics. Flame theories for premixed and diffusion flames. Flame stabilization and combustion instabilities. Solid and liquid propellant combustion. Erosive burning of solid propellant grains. Explosion theories. Detonation theory. Deflagration to detonation transition. _______________________________________________________________________________Top
Historical review : Need for such a study, various flow regimes, fundamental notations, definitions and experimental correlations. Basic relations : Homogeneous, separated and continum mixture approaches for governing equation derivations. Basic parameters and interactions. Transport properties and boundary condition. One-dimensional waves : Continuity and dynamic waves. Pipe flow sedimentary flow, boundary layer motion, flow over body and flat plates, cyclone separators, fluidized beds, gasification and combustion of coal, pneumatic transporters. _______________________________________________________________________________Top
Introduction to hypersonic flight in the atmosphere and the propulsion requirements thereto. Thermodynamic, fluid mechanical, gas dynamic, and thermochemical background for supersonic combustion ramjets. Overall performance considerations of hypersonic propulsion systems and the need for supersonic combustion. Hypersonic airbreathing engine performance analysis. Component performance in inlets, combustors and exhaust nozzles . Other hypersonic airbreathing propulsion concepts, such as the detonation wave engines. Experiments in Structural Mechanics and Stress Analysis. _______________________________________________________________________________Top
Principles of heat transfer: conduction, convection, and radiation. Mass and momentum transfer: elements of mass diffusion and boundary layer theory. Chemical kinetics and equilibrium chemistry. Fundamentals of combustion and flame: premixed flame speed, Burke-Schumann analysis of diffusion flames, and droplet combustion. _______________________________________________________________________________Top
Review of equilibrium gas properties, non-equilibrium and non-equilibrium kinetic theory. Equilibrium flow (Steady shocks, nozzle flow, Prandtl-Meyer flow, Frozen flow) Vibrational and Chemical rate processes (Vibrational rate equation, chemical rate equation, local relaxation times, small departures from equilibrium). Flow with Vibrational and chemical non-equilibrium (Equilibrium and frozen flow, non-linear equators, acoustic equations, speed of sound, sound propagation, small departures from uniform flow, linearised normal shock wave, dispersed shock wave, nozzle flow, MOC). Flow with translational non-equilibrium (transport properties, Bulk viscosity, structure of shock wave, linearised Couette flowe). Radiative transfer in gases (Equation of radiative transfer, radiative equilibrium, radiation-solid surface interaction, Emission and absorption of radiation). Flow with radiative non-equilibrium (Basic non-linear equations, grey-gas, 1D equations, normal shock wave). _______________________________________________________________________________Top
Physics of thermal radiation, methods for evaluation of view factors, radiation exchange between gray, diffuse and partly specular solid surfaces, basic equations for radiation heat transfer in absorbing, emitting and scattering media, radiative properties of molecular gases, spectral models for radiative heat transfer (Narrow Band models, Wide Band models), approximate methods for radiation heat transfer in participating media (optically thick limit, optically thin limit, PN approximtion, SN approximation), treatment of non gray gases. Radiation heat transfer application in space propulsion, microgravity combustion and re-entry problems. _______________________________________________________________________________Top
Variational formulation of the classical theory of isotropic plates, and counterparts for anisotropic, sandwich and layered plates, and plates made up of functionally graded or piezoelectric materials. Combined bending and stretching. Shear Deformation Theories: First-order Theory and Higher-order Theories based on global approximation and discrete layer approaches. Three-dimensional analysis. Comparison of various theories for simple rectangular plate/strip problems. _______________________________________________________________________________Top
Classical bending theory of thin flat rectangular and circular plates and with various edge conditions and loading. Membrane and bending theories of thin shells of revolution. Analysis of circular cylindrical shells. _______________________________________________________________________________Top
Principle of minimum total potential. Principle of minimum complementary potential. Rayleigh-Ritz , Galerkin, Collocation methods, etc. Finite-difference method. Finite element method. Computer based solutions to examples including field problems, nonlinear problems. _______________________________________________________________________________Top
The basic equations of two-dimensional and three-dimensional thermoelasticity. Application of two-dimensional problems of elasticity, thermal stresses in beams, membranes and plates. Thermal buckling. _______________________________________________________________________________Top
Matrix methods of analysis : Stiffness and flexibility. Truss, frame and grid work examples. Finite elements : Discretisation of the continuum, analysis of plane and axisymmetric problems, isoparametric concepts and applications, bending elements. Computer implementation. _______________________________________________________________________________Top
Review of material properties and macro mechanics of composites. Anisotropic theory of elasticity. Plate anisotropic elasticity problems. Analysis of rotating disc. Stress analysis of anisotropic beams, columns, plates and shells. Classical and improved theories of laminated structures. Comparison of the structural behaviour of composite structures with conventional isotropic structure. Vibration and stability analysis. Analysis of wave propagation through composite media. Stress concentration around holes and cut-outs. Stress analysis of bolted and bonded joints. Finite element method of analysis. Analysis of sandwich structures. _______________________________________________________________________________Top
The variational principle and the derivation of the governing equations of static and dynamic systems. Different energy methods : Rayleigh-Ritz, Galerkin etc. Application : Problems of stress analysis, determination of deflection in determinate and indeterminate structures, stability and vibrations of beams, columns and plates of constant and varying cross-sectional area. _______________________________________________________________________________Top
Basics of Damage Tolerance : Strength vs. Damage Tolerance, Historic Introduction and Molecular Interpretation. Mathematical preliminaries : Vectors and Tensors, Complex Variables & Functions, Taylor's and Laurent's Series Expansions, Poles & Residues, Contour Integration Review of Ealsticity: Stress & Strain, Equilibrium, Elasticity, Plasticity and Yield Criteria, Strain Energy, Plane Stress and Plane Strain, Solution methods, Airy stress functions, Complex potentials. Stress Analysis of Cracked Bodies : Stress Concentration in Circular and Elliptic Holes, Stress Intensity Factor, Fracture Modes, Other Analytical, Numerical and Experimental methods. Energy Concepts : Strain Energy Release Rate, J Integral, Virtual Crack Closure, Equivalence of Energy and Stress approaches. _______________________________________________________________________________Top
Programming in C, analog circuits and electronic components, logic gates, introduction to microprocessor architecture, sensors and actuators (transduction principles, energy conversion-motors , solenoids), A/D and D/A conversions, real-time programming concepts, direct digital control implementation, and principles and tools of mechanical design, namely CAD and solid modeling. This course is heavily hands-on project oriented. Laboratory work and small projects will be assigned to help solidify learning throughout the course such as programming, working with microprocessors, and interfacing sensors and actuators. In addition, teams will design, build and demonstrate their solution to the assigned problem. _______________________________________________________________________________Top
Field equations of three dimensional elasticity; Theory of stress and strain, Generalised Hooke's law, comptability conditions, boundary conditions. _______________________________________________________________________________Top
Brief review of vibration of single, multidegree and continuous systems. Introduction to aeroelasticity. General nature and classification of aeroelastic problems. Deformation of aircraft structure under static and dynamic loads. Approximate methods of computing natural mode shapes and frequencies. Steady-state aeroelastic phenomenon with specific reference to wing divergence and control system reversal, solutions to problems of wing divergence and control systems reversal. Flutter phenomenon and fundamentals of flutter analysis. Stability of dynamic systems: Routh- Hurwitz criteria. _______________________________________________________________________________Top
Review of single degree and two-degree freedom systems. Generalised coordinates and Largrange's equation. Normal modes and orthogonality relations. Differential equation, integral equation and energy methods to solutions of beam and plate problems. Introduction to nonlinear and random vibrations. _______________________________________________________________________________Top
Stability of columns: Closed and open sections, flexural, torsional and conbined. Inelastic buckling. Buckling of flat and stiffened plates. Approximate solutins. Rayleigh-Ritz, Galerkin, finite-ddference and finite element methods to determine buckling loads. Crippling of thin-walled sections. Use of master column charts. Introduction to post-buckling of columns and plates, snap buckling of shallow arches and shells. _______________________________________________________________________________Top
Introduction, Review of linear theory of structural mechanics and its foundation. General approach to the formulation and solution of problems of nonlinear structural mechanics involving (a) geometric nonlinearity (b) material nonlinearity and (c) combination of (a) and (b). Brief outline of problems showing the static and dynamic behaviour of plates and shells like large deflection, large amplitude vibration and post-buckling problems of plates (rectangular, circular and skew) and shells (cylindrical and shallow spherical) _______________________________________________________________________________Top
Tensor Algebra, tensor Calculus, Kinematics of Deformation and Motion, Fundamental Laws and Equations (Conservation of mass, conservation of momentum, conservation of energy, restrictions of elastic materials by second law of thermodynamics, constitutive equations) , Linear Elastricity, Kinematics of Fluid Motion, Classical Fluids, Linear Visco-elasticity, Non-linear Elasticity. _______________________________________________________________________________Top
Analysis of indeterminate beams: Clapeyron: S equation for continuous beams - Analysis of frames and rings - Analysis of curved beams - Composite beams. Wide beams - Torsion of noncircular solid and thin-wallved cross - sections, Warping function. _______________________________________________________________________________Top
Review of vibration of discrete and continuous systems-Aspects of nonlinear dynamical system behaviour and solution techniques, some examples like Van der Pol oscillatior, Duffing and Mathieu systems - Introduction to some advanced topics like coupled oscillations, rotating beams, random vibrations, unsteady aerodynamics. Static aeroelasticity, wind tunnel models, divergence instability and aileron reversal - Aeroelastic flutter, stability characteristics and aeroelastic analysis of a typical section, classical flutter analysis and engineering solutions - introduction to nonlinear aeroelasticity. _______________________________________________________________________________Top
Introduction to Friction and Wear, History of Tribology. Elastic Contacts: Elasticity Equations, Hertzian Contacts, Integral Equation Methods. Plasticity: Yield Criteria, Hardness Testing, Shakedown Criteria. Surface Topography: Statistical Characterization, Rough Surface Contact. Friction: Friction Laws, Frictional Contact and Fretting, Frictional Heating. Wear: Wear Models/Maps, Experimental Characterization of Wear. Lubrication: Reynolds Equation, Elasto-hydrodynamic Lubrication. _______________________________________________________________________________Top
Introduction , Basic considerations and definitions. Hypersonic flight paths. Inviscid hypersonic flow theory: Shock expansion method, Surface inclination methods. Small disturbance equations and approximate methods. Similarity laws: Exact methods, Method of chacteristics, Blunt body problem and solution. Method computational methods. Introduction to viscous hypersonic flows. _______________________________________________________________________________Top
Introduction to missiles and launch vehicles, bodies of revolution, non circular shapes, lifting surfaces, low Aspect Ratio characteristics, wing - body - tail interference, prediction of overall characteristics of body dominated configurations and lifting surface dominated configurations, high angle of attack aerodynamics, dynamic derivatives, boundary layer, shock wave - boundary layer interactions aerodynamic heating, intake aerodynamics, engine-airframe integration, airframe flexibility effects on aerodynamics,. Stage separation dynamics. Configuration design methodology of tactical missiles. Design methodology of multistage vehicles. _______________________________________________________________________________Top
Basic features of turbulent flows. Ways of describing turblent flows : Statistical aspects, correlation, spectrum, conditional sampling. Experimental methods : Hot wire anemometer and Laser Doppler anemometer. Equations for compressible turbulent flows. Experimental data on turbulent intensities in some turbulent flows. Prediction of turbulent flows: Statistical theory and its limitations, Integral methods, turbulence modelling, mixing length hypothesis, one-equation and two-equation models, modelling of Reynolds stress. Computer codes and comparison between experimental data and predictions. _______________________________________________________________________________Top
High speed wind tunnels. Special purpose tunnels. Shock tubes, Ballistic ranges. Schlieren, shadowgraph, interferometry. Laser applications. Radiation and spectroscopy. Heat transfer measurements. Analogy techniques. Mechanical vibrations : Accelerometers, frequency analysis. _______________________________________________________________________________Top
- Tensors functions and analysis.
- Random data analysis.
- Homogeneous Isotrophic Turbulence.
- Homogeneous Anisotrophic Turbulence.
- Spectral Analysis and Navier Stokes Equations.
- Turbulence Modeling.
- Second order (Reynolds Stress) Modeling.
- DNS of Turbulent Flows.
- LES of Turbulent Flows.
- Coherent Structures in Turbulent Flows.
- Dynamical Systems approach to Turbulent Flows.
Designing a workable system, Mathematical and system simulation. Optimization, Constrained and unconstrained optimization. Single and multivariable search techniques, Linear, nonlinear and dynamic programming. Optimization of lumped parameter system. Introduction to complex optimization problems. _______________________________________________________________________________Top
Introduction to Acoustic ; Derivation of the wave equation in both cartesian and polar co-ordinates, applications to problems. Fundamentals of Combustion Instability; Basic principles, instability in solid and liquid rockets and ramjets, passive and active control of combustion instability, pulse combustors. Theoretical Analysis of Combustion Instability. Measurement techniques. _______________________________________________________________________________Top
Introduction to Acoustics: Derivation of the governing equations, Lighthill's analogy. Aerodynamic sound in unbounded flows; The Ffowcs Williams - Hawkings equation, vorticity and entropy as sources of sound, sound generation in a fluid with rigid and flexible boundaries, vortex-sound theory of Powell. Aeroacoustics of internal flows; Waves in pipes, Howe's formulation , orifice flows, musical aeroacoustics. Resonant and unstable systems; cavity resonances, edge tones, combustion instabilities. _______________________________________________________________________________Top
Fundamentals of digital data acquisition, Dynamic transducers for transient measurements; Fundamentals of digital image processing, Lasers and laser safety; Principle and application of Particle Image Velocimetry (PIV) and Laser Doppler Velociemtry (LDV); Fundamentals of spectroscopy; Rayleigh scattering; Raman Scaterring, Laaser Induced Fluorescene, and their application in species concentration and temperature measurements. Digital Background oriented Schileren; Optical patternation for spray diagnostics. _______________________________________________________________________________Top
Strain gauges : Mechanical, electrical, acoustic, pneumatic and other types of strain gauges. Associated circuits for electrical resistance strain gauges. Photo-elasticity: Two-dimensional photo-elasticity. Reflection polariscope, photo-stress coats. Analogies : Membrane, electrical analogies. Transducers; Pick-ups to measure displacement, velocity, acceleration and forces. _______________________________________________________________________________Top |