Joel Daou Senior Lecturer (Associate Professor) Qualifications: MSc, PhD (Marseilles). Department of Mathematics University of Manchester, Alan Turing Building Oxford Road , Manchester M13 9PL, UK Room 2.129 (Office hour: Thursday 12pm)

Teaching (Recent):

• Course MATH65031/45031: Stability Theory (Msc + 4th year, 2014-present. Currently  in first semester.)
• Course MATH10232: Calculus and Applications B (2011-present)
• Course MAT35072: Mathematical Modelling, Transport Phenomena and Reactive Flow (3rd year, 2012-14)
• Course MATH60682/MATHT45142: Combustion Theory (Msc + 4th year, 2005-11)
• Course MATH10131: Calculus and Vectors (2010-11)
• Mathematics 2R1/MATH29671 (2nd Year, Series, Laplace Transforms, functions of several variables, 2008-09)
• Course 423/MSC 542: Numerical Solution of Differential Equations (Msc + 4th year, 2002-07)
• Course U213: Hamiltonian dynamical systems (2nd year, 2004-06)
• Course 2Q2:  Further Mathematics for civil engineers (2nd year, 2000-04)

Administrative Roles (Recent):

• Postgraduate (PGR) Director for the PhD programs in Applied Mathematics and Numerical Analysis (Aug 2021-present)
  
• Chair of the Mathematics School Board (2016-2021)
  

Research:

I lead the research activities in the field of combustion in the school of Mathematics at the University of Manchester. This is a fascinating multi-disciplinary area of applied mathematics.

• Fields of competence/research:   Combustion, fluid mechanics, numerical and asymptotic methods, heat and mass transfer, stability theory.
• Major Research topics:  Flame propagation in mixing layers (e.g. triple flames). Ignition and extinction fronts in premixed combustion. Turbulent combustion. Stability of flames. Droplet combustion at high pressure (rocket engines, diesel engines). Convective mixing, ignition and combustion of fuel pockets. Ignition and development of premixed flames under gravity.
• Investigation approach:  numerical and  perturbation methods.

• Publications: see my list of publications 

Selected Publications (Downloadable):

• Daou J.  Effect of Taylor dispersion on the thermo-diffusive instabilities of flames in a Hele-Shaw burner. Combustion Theory and Modelling (2021)
  

• Daou J. and Daou R. Flame Balls in a non-uniform reactive mixture: preferential diffusion, heat-loss and stability. Combustion Theory and Modelling (2019)

• Daou J., Pearce P., and Al-Malki F. Taylor dispersion in premixed combustion: Questions from turbulent combustion answered for laminar fames. Physical Review Fluids (2018)


• Pearce, P. and Daou, J.  Initiation and evolution of triple flames subject to thermal expansion and gravity. Proceedings of the Combustion Institute (2017).

• Daou R., Pearce, P. and Daou, J. Flame balls in non-uniform mixtures. Combustion Theory and Modelling (2016)

• Pearce, P. and Daou, J. Taylor dispersion and thermal expansion effects on flame propagation in a narrow channel. J. Fluid Mech. (2014)

• Daou J. and Daou R. Flame Balls in Mixing Layers. Combustion and Flame (2014).

• Pearce, P. and Daou, J. Rayleigh Bénard instability generated by a diffusion flame. J. Fluid Mech. (2013).

• Al-Malki, F. and Daou, J. Triple-flame propagation against a Poiseuille flow in a channel with porous walls. Combustion Theory and Modelling (2013)

• Pearce, P. and Daou, J. The effect of gravity and thermal expansion on the propagation of a triple flame in a horizontal channel. Combustion and Flame 160 (2013).

• Daou, J. Strained premixed flames: effect of heat-loss, preferential diffusion, and the reversibility of the chemical reaction. Combustion Theory and Modelling 15:437-454 (2011).

• Daou, J. and Al-Malki, F. Triple-flame propagation in a parallel flow: an analytical study. Combustion Theory and Modelling 14:177-202 (2010).

• Daou, J. Asymptotic analysis of flame propagation in weakly-strained mixing layers under a reversible chemical reaction. Combustion Theory and Modelling, 13:189-213 (2009).

• Daou, J., Al-Malki, F. and Ronney, P. Generalized Flames Balls. Combustion Theory and Modelling 13:269-294 (2009).

• Daou, J. Premixed flames with a reversible reaction: propagation and stability. Combustion Theory and Modelling, 12:349-365 (2008).

• Daou, J. and Sparks, P. Flame propagation in a small scale parallel flow. Combustion Theory and Modelling, 11:697-714 (2007).

• Daou, R., Daou, J., and Dold, J. Effect of heat loss on flame edges in a non-premixed counterflow within a thermo-diffusive model. Combustion Theory and Modelling, 8:683-699 (2004).

• Daou, R., Daou, J., and Dold, J. Effect of heat loss on flame edges in a premixed counterflow. Combustion Theory and Modelling 7:221-242 (2003).

• Daou, J., Dold, J., and Matalon, M. The thick flame asymptotic limit and Damkohler’s hypothesis. Combustion Theory and Modelling 6:141-153 (2002).

• Daou, J. and Matalon, M. Influence of conductive heat-losses on the propagation of premixed flames in channels. Combustion and Flame 128:321-339 (2002).

• Daou, J. and Matalon M. Flame propagation in Poiseuille flow under adiabatic conditions. Combustion and Flame 124:337-349 (2001).

• Daou, J. , Matalon M. and Linan, A. Premixed edge flames under transverse enthalpy gradients. Combustion and Flame 121:107-121 (2000).

• Daou, J. and Linan, A. Ignition and extinction fronts in counterflowing premixed reactive gases. Combustion and Flame 118:479-488 (1999).

• Daou, J. and Linan, A. The role of unequal diffusivities in ignition and extinction fronts in strained mixing layers. Combustion Theory and Modelling 2:449-477 (1998).

• Daou, J. Ignition and combustion of fuel pockets moving in an oxidizing atmosphere. Combustion and Flame 115:383-394 (1998).

• Daou, J. and Rogg, B. Convective burning of gaseous fuel pockets and supercritical droplets. Combustion and Flame 115:145-157 (1998).

• Daou, J. and Rogg, B. Influence of gravity on the propagation of initially spherical flames. Proceedings of the Combustion Institute 26:1275-1281 (1996).

• Daou, J., Haldenwang, P. and Nicoli, C. Supercritical burning of liquid oxygen (LOX) droplet with detailed chemistry. Combustion and Flame, 101:153-169, (1995).

Research Projects (for prospective PhD and MSc students, and as 4th year projects)

Several projects are available related to the mathematical theory of flame propagation, a fascinating multi-disciplinary area of applied mathematics involving ordinary and partial differential equations. The approach will typically adopt a combination of analytical techniques (asymptotic methods) and/or numerical techniques (solution of ODEs or PDEs, mostly parabolic and elliptic). The multi-disciplinary experience in combustion involved will be useful for tackling research problems in other fields of application, and wil constitute a valuable asset for jobs in industry (such as the automobile or the aerospace industry). Depending on the preference of the candidate, each of the projects can be tailored in its scope and the methodology of study.

Sample of suggested projects:

• Ignition in a flow field (such as a Poiseuille flow) and in mixing-layers. The main aim is to determine the critical energy of the initial hot kernel (or spark) to ignite a flowing reactive mixture.

• Propagating Flames and their Stability: This  involves the investigation of the various instabilities of flames using analytical and/or numerical approaches. The   flames will be modelled as travelling wave solutions to reaction-diffusion-convection equations, which may, or may not, include full coupling with the hydrodynamics (the Navier-Stokes equation).

• Flame propagation in a multi-scale flow based on a Hamilton-Jacobi type equation (describing the normal propagation of the flame) and comparison with results based on the basic conservation equations.

• Flame initiation and propagation in spatially non-uniform mixtures: This is a problem of considerable interest in combustion, whenever the reactants are spatially separated. The approach will be based on asymptotic and/or numerical methods.  The Combustion basics needed for the projects will be provided and explained to the candidate.

• Laminar aspects of turbulent combustion: The idea is to ask if the fundamental questions of turbulent combustion can be answered for simple laminar flows. Since the answer is often no, we shall formulate and study problems to answer these questions in simpler laminar-flow situations.

• Generalized Flame Balls and their Stability:  Flame balls are balls of burnt gas in a reactive mixture, which constitute stationary solutions to non-linear Poisson's equations. These were first described by the famous Russian physicist Zeldovich (the father of Combustion Theory) about 70 years ago. The fact that these solutions are typically unstable provides a powerful fundamental criterion for successful ignition, i.e. determines the minimum energy (of the spark) required to generate propagating flames. Several projects are available to extend the study of these fascinating flames (mainly their existence and stability) to take into account realistic effects such as the presence of flow-field, non-uniformity of the reactive mixture, proximity of walls, etc. 

• Taylor dispersion in premixed combustion:  In 1953, the British physicist G.I. Taylor published an influential paper describing the enhancement of diffusion processes by a (shear) flow, a phenomenon later termed Taylor dispersion.  This has generated to date thousands of publications in various areas involving transport phenomena, none of which, surprisingly, in the field of combustion. In 1940, the German chemist G. Damköhler postulated two hypotheses which have largely shaped current views on the propagation of premixed flames in turbulent flow fields. The project consists of pioneering investigations linking Taylor dispersion and Damköhler’s hypotheses, and is expected to provide significant insight into turbulent combustion. 

Please contact me for any related query.