This subject aims at providing the students of Mechanical engineering with specific knowledge of computational fluid dynamics for modelling and analysis of the complex fluid-dynamics phenomena occurring in flow machines and internal combustion engines. In particular, focus will be devoted to: - conservation laws and their application to compressible and incompressible flows in one-dimensional pipes; - finite difference methods for the numerical solution of the Euler and Navier-Stokes equations, numerical modelling of travelling shocks in fluids, turbulence modelling and heat transfer.

Familiarity with methods of computational fluid-dynamics and ability to carry out mathematical models for the analysis of the main unsteady events occurring in thermal and hydraulic machines. Skills in the evaluation of the commercial tool performance and in the critical review of the achieved results. Ability to select the correct turbulence model depending on accuracy requirements and available experimental data. Skills in designing mathematical models for both thermal and fluid dynamics characterization of the thermal and hydraulic machines.

Contents of the subject of Thermal and Hydraulic machines.

Analytical models for characterization of energy systems and components. - Mathematical classification of PDEs; hyperbolic, parabolic and elliptic equations of physical interest; theory of the well-posed engineering problem; boundary conditions; system of equations. - Linear advection equation; inviscid, viscous and thermal models; nonlinear equations in fluid-dynamics. - Euler’s equations for one-dimensional flows; wall friction; calculus of the wave propagation speed; method of characteristics for the solution of the Euler equations. General formulation of the conservative equations in the presence of shocks, theory of the boundary conditions for wave propagation problems. - Shock velocity and Rankine-Hugoniot jump conditions. - Statistical analysis of turbulent flows, Reynolds-Averaged Navier-Stokes (RANS) equations. Mathematical closure of turbulence models: one- and two-equation models. Large Eddy Simulation (LES) approach. Methods for the numerical computation of flows - Finite difference methods for unsteady flows: explicit and implicit difference formulas, upwind e centered schemes; numerical accuracy of methods; the concepts of consistency, stability and convergence; Lax’s theorem for convergence of numerical solutions and general formulation of Von Neumann’s method to evaluate the stability of numerical schemes; spectral analysis of numerical errors. - Finite volume method and conservative differentiation: numerical fluxes in convection and diffusion equations; Lax-Friedrichs and Lax-Wendroff schemes; - Riemann’s problem and high-resolution numerical schemes to reduce numerical oscillations in the presence of flow discontinuities (such as aerodynamic shocks or cavitation collapse); Godunov methods. Flux-Difference vs. Flux-Vector Splitting methods. - Numerical methods for turbulent flows. - Applications of the developed concepts to the numerical simulation of: unsteady processes in induction and exhaust systems of internal combustion engines, pressure waves and shock propagation in 1D lines, turbulent flows and acoustic cavitation problems. Applied lectures and Laboratory work programme. Numerical and graphic exercises are carried out, involving: evaluation of numerical stability, spectral error analysis, effects of conservativeness in the simulation of shock waves. The students are requested to model 1D or 2D processes by using homemade or commercial tools.

The subject consists of lectures and applied lectures.

Notes, diagrams and charts are available to students at the end of the lecture. When available, Powerpoint slides in pdf format through the subject web page. For further reference and reading students may consult the followings: - R.J. Leveque, “Finite Volume Methods for Hyperbolic Problems”, Cambridge University Press, N.Y., 2002. - J.C. Tannehill, D.A. Anderson, , R.H. Pletcher, “Computational Fluid Mechanics and Heat Transfer”, second edition, McGraw-Hill, N.Y., 1997 - C. Hirsch, “Numerical Computation of Internal and External Flows” Vol. 1: Fundamentals of Numerical Discretization, John Wiley & Sons, - Eleuterio F. Toro “Riemann Solvers and Numerical Methods for Fluid Dynamics”, Springer-Verlag, Berlin, 1997 - A.E. Catania, A. Ferrari, M. Manno, “Development and Application of a Complete Multijet Common-Rail Injection System Mathematical Model for Hydrodynamic Analysis and Diagnostics”, ASME Paper ICES2005-1018, 2005. - A.E. Catania, A. Ferrari, M. Manno, E. Spessa, “A Comprehensive Thermodynamic Approach to Acoustic Cavitation Simulation in High-Pressure Injection Systems by a Conservative homogeneous Two-Phase Barotropic Flow Model”, ASME Transactions, Journal of Engineering for Gas Turbines and Power, Vol 128, pp.434-445, 2006.

Modalità di esame: Prova orale obbligatoria; Elaborato scritto individuale;

The students are requested to take an oral examination based on the lectures as well as on the assessment of the applied lectures and laboratory work carried out during the semester. The maximum mark is 30/30 cum Laude.

Modalità di esame: Prova orale obbligatoria; Elaborato scritto individuale;

The students are requested to take an oral examination based on the lectures as well as on the assessment of the applied lectures and laboratory work carried out during the semester. The maximum mark is 30/30 cum Laude.