University of Zaragoza, Spain
Cesar Dopazo is Honorary Professor at the University of Zaragoza, Spain, where he teaches Fluid Mechanics at graduate and postgraduate level. His research interests span a wide variety of topics, including: mixing and combustion; intermittency in turbulent shear flows; multi-phase flows (including the derivation of the two-phase flow equations using a statistically conditioned averaging formalism); PDF transport methods for turbulent flows; the local geometry of iso-scalar surfaces and its influence in mixing and chemical reaction; cavitating bubble dynamics; and energy modeling and planning.
Professor Dopazo graduated as an Aeronautical Engineer from Madrid Polytechnic University in 1969. He then pursued doctoral degrees at the State University of New York, Stony Brook (PhD in Mechanical Engineering). He was Postdoctoral Research Associate at Johns Hopkins University. He was Associate Scientist at Brookhaven National Laboratory (US Department of Energy), and then became a Technical Advisor. On his return to Spain, and following a brief spell at UNESA (Spanish Electric Utilities Consortium), he was appointed Professor of Fluid Mechanics at the University of Zaragoza. He has been recently appointed Distinguished Scholar by the Johns Hopkins University.
He is a founding Academician of the Royal Academy of Engineering (Spain); he was the promoter and founding director of LIFTEC, one of the main combustion research laboratories in Spain; he was General Director of CIEMAT, the Spanish National Laboratory on Energy and Environmental Research (Spanish Government, Madrid); and he has served as a member of the High Level Group on Hydrogen of the European Commission, and as an advisor on Energy and Climate Change to EC President J.M.D. Barroso.
He is the author of over 130 publications, and has supervised 13 PhD theses. He has participated, often as principal investigator, in more than 50 research projects and technology transfer contracts, many of them for the European Commission and other international institutions.
The deformation and rotation of fluid line, area and volume elements embedded in turbulent premixed flames are summarized. Special attention is given to the volumetric dilatation rate per unit volume, ∇⋅u,and to the local strain rates normal, aN , and tangential, aT , to iso-scalar surfaces. u is the local flow velocity. Their variations across the flames brush, obtained from DNS, are shown for various flames. Transport equations for ∇⋅u, aN and aT are discussed.
Deformation and rotation of non-material elements are analyzed. The volumetric dilatation rate, ∇⋅uc , and the total normal and tangential strain rates, aN + ∂Sd / ∂xN and aT + 2kmSd, are also investigated and their variation across the flame is presented for various flames. uc = u + Sd n is the local velocity of a point on the iso-surface c(x,t) = γ , Sd is the displacement speed relative to the fluid of the iso-surface, n is the unit vector normal to the iso-surface, c(x,t) is the reaction progress variable, 0 ≤ γ ≤ 1 is a constant value, xN is the local coordinate normal to the iso-surface, positive in the direction of n, and km is the local mean curvature of the iso-surface.
Conjectures on relevance of (aN + ∂Sd / ∂xN)-1 as a possible characteristic mixing time and as a parameter related to local quenching are discussed.