HEat (and Mass) Transfer in Turbulent Sprays - HETS

Principal Investigator:
Luca Brandt

Department of Mechanics, KTH, Royal Institute of Technology (Sweden)

Local Project ID:

HPC Platform used:
Hazel Hen of HLRS

Date published:

The focus of this project is the direct numerical simulation (DNS) of an evaporating spray in a turbulent channel flow. The complexity of the phenomenon lies in the nonlinear interaction of phase change thermodynamics and turbulent transport mechanisms at a multitude of scales. The recent availability of larger supercomputing power, together with our novel technique to treat efficiently the interface resolved phase change, enables us to perform the first DNS of more than 14k droplets evaporating in turbulent flow, with full coupling of momentum, heat and mass transfer, both intra- and inter-phase.


Droplets evaporating in a carrier fluid are encountered in a variety of engineering processes of great practical importance, like aerosols, spray dryers and most importantly combustion of liquid sprays. The topic is of strong relevance to answer two important societal challenges: secure, clean and efficient energy and smart, green and integrated transport.

The physical problem involves a series of phenomena, such as clustering of droplets, modulation of turbulence induced by the dispersed phase, evaporation thermodynamics, turbulent mixing of chemical species, inter-phase heat transfer, which are entangled in a complex way and at multiple scales. A thorough understanding of the rate-limiting processes that govern these intricate physics is still lacking, but is crucial towards the goal of efficient combustion and reduction of pollutant emissions.

The computational effort required to perform first-principles direct numerical simulations (DNS) of a fully resolved fluid phase dispersed in a turbulent carrier flow (such as sprays or particle suspensions) has been prohibitive until very recent years. The additional complexity emerging from phase-change thermodynamics, resulting in droplet size variations and interplay of different transport mechanisms, represents a considerable step beyond what has currently been achieved with DNS.

The present project is the first venture of DNS in the field of large scale turbulent evaporating sprays, and as such represents a pioneering effort in the simulation of energy relevant flows, marking a milestone as research moves beyond single droplet studies and experiment-based correlations.

Results and methods

We simulate a turbulent channel flow of n-heptane evaporating in nitrogen, with different wall boundary conditions (isothermal and adiabatic), in an environment that reproduces the pressure and temperature conditions relevant in internal combustion engines (around 40 bar and 1000 °C). The dispersed phase is constituted by more than 14000 individual droplets, each fully resolved with a grid resolution of 24 points per initial diameter.

The most important simplifying assumptions are spherical shape of the droplets and no break-up or coalescence of the liquid phase. These are fully valid in the evaporation regime of most relevant combustion applications (common rail diesel injectors for example), where the droplets are sufficiently small and the surface tension force larger than inertia and viscous forces (small Capillary and Weber numbers). The numerical method has been developed and validated by the research team, and is based on the Immersed Boundary technique, allowing for accurate and computationally efficient phase coupling and calculation of the phase change.

Four-way coupling of the droplet motion with the turbulent carrier phase and interface-resolved evaporation dynamics allow us to draw a qualitative and quantitative comparison with large-eddy simulations coupled with Lagrangian particle tracking (LES/LPT) of the same flow configurations, pointing out the mechanisms that cause the LES/LPT to deviate from the DNS. As LES/LPT is currently the state of art for the numerical simulation of turbulent spray evaporation in realistic flow configurations, due to favourable trade-off between accuracy and computational affordability, our effort leads the way to identify the shortcomings of the LES/LPT approach and suggest the targets where improvements of the current LPT closures are most needed.

On-going Research and Outlook

Follow-up of the project will be the investigation of different flow parameters and configurations, and the introduction of multicomponent evaporation, which is a critical topic in view of the recent surge in the usage of fuel and biofuel blends. Concurrently, the insight gained through the analysis of the DNS databases will be leveraged towards the development of more accurate LES/LPT models for evaporating turbulent sprays.


C. Duwig, G. Lupo, A. Gruber, L. Brandt, P. B. Govindaraju, T. Jaravel, M. Ihme, Direct numerical simulation, analysis, and advanced modeling of the evaporation of multiple fuel droplets in a hot turbulent flow, Proceedings of the Summer Program 2018, Center for Turbulence Research, Stanford University (2018) 319–328.

G. Lupo, M. Niazi Ardekani, L. Brandt, C. Duwig, An Immersed Boundary Method for flows with evaporating droplets, Submitted for publication (2019).

P. Costa, F. Picano, L. Brandt, W. P. Breugem, Universal scaling laws for dense particle suspensions in turbulent wall-bounded flows, Physical Review Letters 117 (2016) 134501.

Research Team

Giandomenico Lupo, Mehdi Niazi Ardekani, Christophe Duwig, Andrea Gruber, Luca Brandt (PI)

Scientific Contact

Prof. Luca Brandt
Linné Flow Center, Department of Mechanics
KTH, Royal Institute of Technology
SE-100 44 Stockholm (Sweden)
e-mail: luca [@]

NOTE: This project was made possible by PRACE (Partnership for Advanced Computing in Europe) allocating a computing time grant on GCS HPC system Hazel Hen of the High Performance Computing Center Stuttgart (HLRS), Germany.

HLRS project ID: PP16153682

January 2019