3rd Cycle of Studies

### (351) Advanced fluid mechanics

**Part I. ***Incompressible flow*

1. Recapitulation of flow field description equations. 2. Perturbation theory and transition from laminar to turbulent flow. 3. Derivation and solution of the Orr-Somerfeld equations. 4. Modelling of transition. 5. Transitional flows on flat plates, airfoils and aircraft wings. 6. Fully turbulent flows. Statistical analysis of turbulence. 7. Turbulence parameters and properties. 8. Reynolds-stress tensor. Turbulence scales. 9. Governing equations for turbulent flows. 10. Turbulence modelling. Zero, one, and two-equation turbulence models. Non-linear turbulence models. Reynolds-stress models.

**Part II.** *Compressible flow*

1. Recapitulation of the essentials of two-dimensional compressible flows. 2. Supersonic and hypersonic flows. 3. Newton theory. 4. Very high temperature flows. 5. Low density fluid flows.

### (355) Computational Fluid Dynamics (CFD)

1. Introduction. Error analysis. Essential algorithms for the solution of equation systems and numerical integration. 2. Linear and non-linear differential equations. Classification of differential equations governing mass transfer and heat transfer phenomena. Typical equations governing convection and diffusion problems. The “source term” concept. The importance of boundary conditions and initial conditions. Coupling of purely mathematical analysis of differential equation initial and boundary conditions with those of mass transfer problems. 3. Discretization techniques of differential equations. Taylor expansion. Discretization of first and second order. Complex forms of equation discretization. Error analysis of discretized equations. 4. Finite differences method. Techniques for the solution of parabolic, elliptic and hyperbolic flow problems with the use of finite differences. Discretization techniques for compressible flow problems. 5. Finite volumes method. Numerical integration on a control volume. Control volume techniques adapted for specific problems. The numerical scheme and the interpolation scheme on the control volume technique. The hybrid and the central scheme. Higher order numerical schemes. The SIMPLE and SIMPLEC pressure correction technique. 6. Elements from grid generation theory. Classification of grids and grid quality. Grid transformation from the cartesian to the generalized curvilinear space. Transformation of the fluid flow and heat transfer cartesian equations to the generalized curvilinear coordinate system. The Jacobi determinant and its importance on grid transformation and finite volume numerical integration. 7. Elements of vector programming. Management of vector units on the computer processor. Programming on a parallel environment for high performance computing. The MPI parallel programming protocol.

### (389) Aerodynamic Design and Control of Aircraft

Introduction, history of aeronautics, aerodynamic coefficients, lift generation, finite span wings and downwash, compressibility effects, drag, types of drag, drag polar, moments. Propulsion, internal combustion engines and turbo engines, propellers, Breguet equation. Flight mechanics, equations of motion, straight level flight, required thrust, available thrust and maximum speed, required power, available power and maximum speed, minimum speed, stall and lift devices (flaps, slats), climb rate, service and absolute ceiling, time to climb, maximum range and flight endurance, minimum turning radius, takeoff, landing. Stability, static and dynamic stability, longitudinal stability, contribution of the main wing, tail and fuselage, directional stability, equations of motion and stability derivatives, automatic control. Aircraft design: conceptual design, weight estimation, performance parameters, configuration layout, preliminary design, regulations, control surfaces design, trimming, aerodynamic optimization, winglets, V-n diagram, engine/propeller selection, vents design.

### (315) Thermal Turbomachinery

Conceptual, preliminary, detailed design. Specific aerodynamic data for aircraft wings. Aircraft performance (takeoff, climb, steady level flight, landing). Aircraft stability and control. Future designs. Aircraft design examples. Aerothermodynamics for reentry conditions. Operation of aeroengines. Configuration of engines and cycles for various aeronautical applications. Design and development of modern propulsion units. Study of their behavior under specific flight conditions (takeoff, climb, landing, straight horizontal flight). Pollutant and noise emissions in the atmosphere and in urban regions.

### (326) Experimental Fluid Mechanics

Measurement theory, applied to fluid mechanics. Analysis of measurement error and uncertainty assessment methods. Pressure measurement methods. Flow rate measurement methods. Flowmeters. Measurement regulations. Velocity and turbulence measurements in fluid mechanics systems. Laser-Doppler Anemometry measurements. Flow visualization methods. Design of experiments for comparison with computations. Use of computers and automation for the measurement of fluid mechanical quantities.

### (387) Aeroengine Technology

Historical development of aircraft engines. Defining parameters of required thrust for the execution of aircraft missions. Engine operation and thermodynamic cycles. Architecture, components and non-rotating parts. Demands and technological limits according to mission phases. Pollution and noise pollution. Thermal-mechanic endurance. Optimization of construction and operation. Future modifications and innovations.