


Politecnico di Torino  
Academic Year 2014/15  
01NMILO Computational fluid dynamics for thermal engines 

Master of sciencelevel of the Bologna process in Automotive Engineering  Torino 





Subject fundamentals
The module aims at providing the students of Automotive Engineering with specific knowledge of computational fluid dynamics for modelling and analysis of the complex fluiddynamics phenomena occurring in automotive internal combustion engines. In particular, focus will be devoted to:
conservation laws and their application to intake and exhaust piping systems, injection apparatuses and combustion chamber; finite difference methods for the numerical solution of the Euler and NavierStokes equations, numerical modelling of travelling shocks in fluids, turbulence and heat transfer. 
Expected learning outcomes
Familiarity with methods of computational fluiddynamics and ability to carry out mathematical models for the analysis of the main unsteady events occurring in internal combustion engines.
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 engine, including the cooling system. 
Prerequisites / Assumed knowledge
The knowledge on the motor vehicle architecture

Contents
Analytical models for characterization of engine systems and components
Mathematical classification of PDEs; hyperbolic, parabolic and elliptic equations of physical interest; theory of the wellposed engineering problem; boundary conditions; system of equations. Linear advection equation; inviscid, viscous and thermal models; nonlinear equations in fluiddynamics. Eulers equations for onedimensional flows; wall friction; calculus of the wave propagation speed; method of characteristics for the solution of the Eulers equations. General formulation of the conservative equations in the presence of shocks, theory of the boundary conditions for wave propagation problems. Shock velocity and RankineHugoniot jump conditions. Statistical analysis of turbulent flows, ReynoldsAveraged NavierStokes (RANS) equations. Mathematical closure of turbulence models: one and twoequation 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; Laxs theorem for convergence of numerical solutions and general formulation of the Von Neumanns 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; LaxFriedrichs and LaxWendroff schemes; Riemann's problem and highresolution numerical schemes to reduce numerical oscillations in the presence of flow discontinuities (shocks, cavitation); Godunov methods. FluxDifference vs. FluxVector Splitting. Numerical methods for turbulent flows. Applications of the developed concepts to the numerical simulation of: unsteady processes in induction and exhaust engine systems, pressure wave and shock propagation in 1D lines, turbulent flows, acoustic cavitation occurrences, heattransfer to the engine cooling system. 
Delivery modes
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 simple engine processes by using homemade or commercial tools. 
Texts, readings, handouts and other learning resources
Notes, diagrams and charts are available to students at the end of the lecture. When available, Powerpoint slides in pdf format through the course 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, McGrawHill, 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, SpringerVerlag, Berlin, 1997 A.E. Catania, A. Ferrari, M. Manno, Development and Application of a Complete Multijet CommonRail Injection System Mathematical Model for Hydrodynamic Analysis and Diagnostics, ASME Paper ICES20051018, 2005. A.E. Catania, A. Ferrari, M. Manno, E. Spessa, A Comprehensive Thermodynamic Approach to Acoustic Cavitation Simulation in HighPressure Injection Systems by a Conservative homogeneous TwoPhase Barotropic Flow Model, ASME Transactions, Journal of Engineering for Gas Turbines and Power, Vol 128, pp.434445, 2006. 
Assessment and grading criteria
The students are requested to take an oral examination based on the lectures as well as on the assessment of the applied lectures carried out during the course.

