Checking date: 23/04/2025 10:13:38


Course: 2025/2026

Combustion
(12466)
Máster Universitario en Matemática Industrial (RD 1393/2007) (Plan: 330 - Estudio: 258)
EPI


Coordinating teacher: VERA COELLO, MARCOS

Department assigned to the subject: Thermal and Fluids Engineering Department

Type: Electives
ECTS Credits: 6.0 ECTS

Course:
Semester:




Requirements (Subjects that are assumed to be known)
Ordinary Differential Equations / Dynamic Systems Partial Differential Equations The student should have studied, or be studying, the Basic Modeling course
Objectives
COMPETENCES To acquire and understand knowledge that provides a foundation or opportunity to develop and/or apply original ideas in the field of combustion processes and reactive flows, with the ability to translate industrial needs (e.g., in energy, transport, or safety sectors) into R&D&I projects involving the mathematical modelling of combustion. To apply acquired knowledge on conservation equations, chemical kinetics, flame propagation, droplet and spray combustion, and combustion instabilities, and to demonstrate the ability to solve problems in new or unfamiliar environments, including integration into multidisciplinary R&D&I teams in industrial or academic settings. To effectively communicate conclusions, along with the underlying knowledge and reasoning, on the behaviour of complex reactive systems, both to specialized audiences (engineers, combustion scientists, numerical modellers) and non-specialists (innovation managers, safety officers, policy makers), clearly and unambiguously. To possess the learning skills necessary to continue studying autonomously, especially on advanced topics related to turbulent combustion, nonlinear reaction systems, or coupled flow-reaction-heat phenomena, and to be prepared to pursue doctoral studies in these areas. To achieve a sound basic knowledge in an area of Engineering/Applied Sciences such as combustion, as a starting point for its mathematical modelling, both in well-established contexts (laminar flames, detonations, homogeneous combustion chambers) and in new or multidisciplinary environments (combustion in turbulent flows or with fuel atomization). To model specific ingredients of combustion (multicomponent mixtures, kinetic mechanisms, transport effects), and apply appropriate simplifications that enable numerical treatment without compromising the accuracy or relevance of the results, in accordance with the requirements of the physical or industrial system. To validate and interpret results obtained from mathematical models of combustion, comparing them with experimental visualizations, laboratory measurements, or theoretical predictions, and to extract useful conclusions for the design or operation of real systems. To model complex systems such as counterflow diffusion flames, spontaneous ignition in confined enclosures, or turbulent combustion regimes, formulating well-posed problems from mathematical, physical, and computational perspectives. LEARNING OUTCOMES To understand some of the most complex problems related to combustion in the context of engineering and applied sciences, including the interplay of chemical reactions, mass and heat transport, and turbulence. To be able to mathematically model complex elements of combustion, such as flame fronts, detonations, or droplet and spray combustion, understanding the level of approximation and assumptions made in each case. To comprehend the challenges posed by both the numerical simulation and theoretical analysis of combustion models, including stiffness, multiscale behaviour, and sensitivity to thermochemical and kinetic parameters.
Description of contents: programme
1. Introduction - Historical Perspective - The science of combustion - Future Developments 2. Conservation equations for reactive flows - Multicomponent mixtures * Mass fractions * Molar fractions * Molar concentrations - Equations of state for ideal gas mixtures * Thermal equation of state * Caloric equation of state - Molecular transport in multicomponent mixtures * Diffusion velocities * Multicomponent transport * Usual simplifications in combustion problems - Conservation equations * Mass * Linear momentum * Species * Energy - Characteristic scales and dimensionless numbers 3. Thermochemistry - The assumption of complete combustion * Stoichiometric mixture * Equivalence ratio * Composition of the product mixture in complete combustion + Lean combustion + Rich combustion - Adiabatic flame temperature * Definition * Heat of combustion * Calculation of the adiabatic flame temperature + Variable cp + Constant cp - Complete combustion vs. incomplete combustion * Major and minor species - Chemical equilibrium in reactive mixtures * The equilibrium constant * Dissociation of the major species * Effect of temperature and pressure 4. Combustion kinetics - Chemical kinetics * Types of elementary reactions * Detailed and reduced mechanisms * One-step mechanism * The limit of high activation energy - Rate of heat release by chemical reaction - Steady state assumption - Partial equilibrium assumption - Examples * Hydrogen combustion * Hydrocarbon combustion * Zeldovich analysis for the production of NOx 5. Combustion in systems with homogeneous composition - Conservation equations for systems with homogeneous composition - Adiabatic combustion in a well-stirred reactor. Steady solutions * The number of Damköhler * Ignition and extinction: The S-shaped curve - Frank-Kamenetskii theory of thermal explosions - Chain-branching explosions * Explosion limits in H2-O2 mixtures * Explosion limits in HC-O2 mixtures - Spontaneous ignition in a combustion chamber with variable volume - Other ignition processes 6. Fronts reagents: Detonation and deflagration - Rankine-Hugoniot relations - Detonation * ZND Structure * Galloping "detonations" * Actual structure of detonations - Deflagrations or premixed flames * Internal structure * Laminar flame speed + Variation with pressure and equivalence ratio * Minimum Ignition Energy * Quenching distance * Flammability limits 7. Diffusion Flames - non-premixed combustion - Relevant thermochemical parameters - The limit of infinitely fast reaction - Finite-rate effects * Counterflow diffusion flames * Ignition and extinction: The S-shaped curve - Examples * Jet diffusion flames * Non-premixed flame-vortex interactions 8. Evaporation and combustion of droplets and sprays - Droplet evaporation - Droplet combustion - Homogenised description of spray combustion 9. Combustion instabilities - Flame stretch and curvature - Thermo-diffusive instability - Hydrodynamic instability - Thermoacoustic instability 10. Turbulent combustion - Premixed turbulent combustion * Characteritis scales * Diagram of regimes * Turbulent flame speed - Non-premixed turbulent combustion * Characteritis scales * Diagram of regimes * Turbulent jet diffusion flames
Learning activities and methodology
Use of board for discussion of theoretical concepts and illustrative examples.
Assessment System
  • % end-of-term-examination 0
  • % of continuous assessment (assigments, laboratory, practicals...) 100

Calendar of Continuous assessment


Basic Bibliography
  • A. Liñán & F. A. Williams. Fundamental Aspects of Combustion. Oxford University Press. 1993
  • D. A. Frank-Kamenetskii. Diffusion and Heat Transfer in Chemical Kinetics. Plenum Press. 1969
  • D. E. Rosner. Transport Processes in Chemically Reacting Flow Systems. Dover. 2000
  • F. A. Williams. Combustion Theory. Benjamin-Cummings. 1985
  • N. Peters. Turbulent Combustion. Cambridge University Press. 2000

The course syllabus may change due academic events or other reasons.