Introduction. Instructor, student reception, examinations. Educational and professional objectives and approaches to rocket propulsion. Study tips, material and grading.Useful background material. Reference texts.

Vector Analysis. Scalars, vectors and tensors in finite-dimensional spaces and their combination laws, component representation and change-of-basis; transpose, inverse, symmetric and orthogonal tensors; 1D and 2D invariant subspaces; canonic representation and quadratic forms of symmetric tensors. Vector differentiation; curves and surfaces; the del operator; differentiation rules; vector integration, divergence, Stokes', Gauss and Green's theorems; curvilinear coordinates.

Complex Analysis. Complex numbers, Cartesian and polar representations, complex powers, roots and functions; continuity and limits, derivatives, Cauchy-Riemann equations, analytic and harmonic functions; elementary functions (exponential, logarithmic, complex power, trigonometric, hyperbolic), mappings.

Special Functions. Complex quasi-linear 1st and 2nd order ordinary differential equations, linear independence, homogeneous solutions, Frobenius method, particular solutions; Gamma function; separation of variables in cylindrical and spherical coordinates; Bessel and Legendre functions; 2nd order homogeneous Sturn-Liouville boundary value problems; eigenvalues, eigenfunctions and their properties; non homogeneous problems.

Thermodynamics. General principles and thermodynamic equilibrium, alternative formulations, thermodynamic derivatives, ideal gases, real gases, thermodynamic processes, thermal engines, scales of temperature, thermodynamic cycles, thermodynamic stability.

Thermochemistry. Equilibrium of single and simultaneous chemical reactions, chemical equilibrium in ideal gases, thermodynamic data, formation properties, heats of reaction, adiabatic and nonadiabatic reaction, parametric dependence, reactions in real gases. Speed and reaction mechanisms, reaction constants, reactions order and molecularity, in the 1st and 2nd order consecutive reactions, competitive and opposite chain reactions, explosive reactions, reaction times.

Heat Conduction. The heat conduction equation; steady conduction networks; 1D steady conduction; quasi-1D steady conduction, fins; 1D unsteady conduction, semi-infinite and finite-thickness flat walls; 1D unsteady ablation.

Flow Equations. Coordinates, kinematics, conservation and constitutive equations, special forms of the conservation equations, transport properties, boundary conditions, fluid dynamic similarity. 

Linear Waves. Small amplitude waves, fans, the wave equation, plane waves, planar and spherical harmonic waves, generation of sound (monopoles, dipoles, quadrupoles), waves through different media, standing harmonic waves, waveguides, acoustic dampers.

Laminar Viscous Flows. Developed flows in pipes, shear flows, flows around cylinders and spheres, boundary layers, parameters and integral equations. Quasi-parallel incompressible flows: two-dimensional and axisymmetric boundary layers, jets, wakes and shear layers. Quasi-parallel compressible flows: two-dimensional and axisymmetric boundary layers, stagnation flows, the Newtonian theory.

Flow Stability and Transition. Nonlinear dynamic effects; linear stability of parallel flows, Reynolds and Orr-Sommerfeld equations; turbulent transition, development, parametric dependence, prediction.

Turbulent Flows. Fourier analysis, probability, random variables and processes. Incompressible turbulent flow analysis, equations, turbulent kinetic energy, two-dimensional and axisymmetric boundary layers, flows in ducts, free jets, turbulence models. Compressible boundary layers.

Fundamentals of Rocket Propulsion. Rocket propulsion systems and technologies; mass, momentum and energy balances; free rocket performance; performance parameters; single and multistage rockets; optimization of multistage rockets; electrical rocket optimization.

Space Shuttle Mission. Space shuttle system; navigation and flight; guidance, navigation and control; ascent to orbit, orbital operations and maneuvers; re-entry; landing; on-orbit functions and requirements.

 Space Shuttle Propulsion. Propulsion system: Space Shuttle Main Engine (SSME), external tank, solid rocket boosters, main propulsion subsystem, orbital maneuver subsystem, reaction control system; SSME combustion devices, powerhead, igniters, preburners, injectors, combustion chamber and nozzle; SSME heat transfer.

 SSME Turbomachinery. SSME turbopumps, operation, parameters and design, cavitation and suction performance; SSME turbines, operation, parameters and design; vehicle/engine requirements; low/high pressure oxidizer/fuel turbopumps; selection, design, architecture, development; axial balance; bearings and seals, critical speeds, rotodynamics; development problems and solutions.

Mission Analysis. Atmosphere, orbital mechanics, elliptical orbits, disturbances, maneuvers, impulsive and low thrust transfers, launch, ascent into orbit, re-entry in the atmosphere.

Chemical Rocket Performance. Characteristic performance parameters; nozzles: optimal expansion, configuration of the flow, bell nozzles, operational limitations, optimization, non-conventional nozzles; cold gas rockets.

Solid Propellant Rockets. Architecture, generalities and classifications; solid propellants, combustion, instabilities, ignition transients, two-phase flow effects, heat transfer, thermal protections.

Liquid Propellant Rockets. Architecture, general and classifications; liquid propellants, mono-, bi-and tri-propellant, combustion, performance, effects of non-equilibrium, injection, sizing of the combustion chamber, instability (injection and thrust coupling mechanisms), propellant management and cycles, tanks and propellant sloshing, regenerative cooling.

Hybrid Rockets. Generalities, speed of regression and its axial distribution, the oxidizer/fuel ratio, length of grain, combustion history, chamber pressure, thrust, grain temperature effects, thermal radiation and the speed of reaction.

Heat Radiation. Electromagnetic radiation; thermal radiation; thermal radiation of materials; radiation networks; radiation properties of gases; radiation networks in gases.

Turbomachines. General information, types and architectures, Euler equation, efficiencies,. Stresses and materials, velocity triangles, characteristic parameters, similarity; turbopumps, inducers, compressors, turbines and hydraulic turbines. Axial machines: flow velocity, bladings, fluid forces on profile cascades, losses; compressors: flow instabilities; turbines: degree of reaction, chocked distributors, stagnation temperatures. Radial machines: radial cascades, slip velocity.

Cavitation and Two-Phase Flows. General, conservation and constitutive equations, phase changes, boiling and cavitation, nucleation, bubble dynamics, cavitation forms and similarity parameters, patterns of liquid/gas, liquid/gas/vapor and liquid/vapor flows, thermal effects, simulation of cavitating flows.

Cavitating Turbopumps. Characteristic and similarity parameters, pumping and suction performance, thermal cavitation. Instabilities induced by cavitation: classification and characteristics, rotating cavitation, self-induced oscillations, rotordynamic forces, flow fluctuations of the feed system, propulsively coupled oscillations (POGO)

The Course provides an in-depth treatment of classical and state-space approaches to the analysis of dynamic systems. It deals with the modelling, the analysis and the stability/performance characterisation of open-loop dynamic systems, with particular attention to aerospace case studies. A specific part of the course is also dedicated to the use of Matlab-Simulink CAE tools for the dynamic systems analysis.

The course focuses on the physical phenomena and analytical procedures required to understand and predict, to first order, the behavior of orbiting spacecraft. The main aim is to provide suitable application tools and illustrate the main methodologies, both from a theoretical and a practical viewpoint, required to tackle a mission analysis in terms of orbital mechanics and attitude control.

Il corso intende fornire allo Studente le nozioni essenziali relative agli aspetti fisici della Meccanica del Volo dei velivoli ad ala fissa ed ai relativi modelli matematici e numerici.

Fanno parte del corso l'analisi delle prestazioni classiche dei velivoli da trasporto propulsi a getto e ad elica, lo studio dell'equilibrio della macchina in condizioni di volo rettilineo e curvo, la regolazione della traiettoria da parte del pilota tramite i comandi di volo, le nozioni di base relative alla risposta dinamica del velivolo ai comandi del pilota.

Periodo e crediti: primo e secondo periodo, 12 CFU

Contatti: Prof. Alessandro Quarta