Thermodiffusive Instabilities in Lean Premixed Hydrogen/Air Flames

Principal Investigator:
Prof. Heinz Pitsch

RWTH Aachen

Local Project ID:

HPC Platform used:
SuperMUC-NG at LRZ

Date published:


The recent rise of renewable energy sources is promoting the use of hydrogen as a carbon-free energy carrier. One possibility to harness the energy stored in hydrogen is its usage in thermochemical energy conversion processes such as in gas turbines, industrial burners, or internal combustion engines. However, lean hydrogen/air flames are prone to intrinsic combustion instabilities and, in particular, thermodiffusive instabilities, which can substantially change flame dynamics, heat release rates, and flame speeds. These aspects are highly relevant for the safe operation of any combustion device, e.g., to avoid flame flashback, but can also increase thermal efficiencies. Thermodiffusive instabilities originate from the low Lewis number of hydrogen, which represents the ratio of the thermal and mass diffusivity, where the latter is particularly high for hydrogen.  The strong differential diffusion of hydrogen leads to an amplification of small flame front perturbations such that strongly wrinkled flame fronts are observed with a significantly enhanced flame speed and strong variations of the local reaction rates. For example, thermodiffusive instabilities can lead to four times higher flame speeds compared to the unstretched laminar burning velocity in laminar lean hydrogen/air mixtures at ambient conditions [2].

While thermodiffusive instabilities have been extensively studied in laminar flows, combustion applications typically feature interactions of a flame with a turbulent flow, necessitating a comprehensive understanding of thermodiffusive instabilities in turbulent flows. Theoretical works expect flame intrinsic instabilities to be particularly relevant for low Karlovitz numbers, but the exact region of influence in the turbulent combustion regime diagram and the identification of all relevant parameters is yet unclear. However, the effects of differential diffusion and, hence, thermodiffusive instabilities are found to be sustained in turbulent flames for a large range of Reynolds and Karlovitz numbers [3],  so it is fundamental to further understand the mutual interaction between turbulence and thermodiffusive instabilities to incorporate these effects into combustion models for predictive simulations of hydrogen flames.

In particular, the development process of combustion devices typically involves the use of simulations, e.g. Large Eddy Simulations (LES), to cut the high cost associated with experimental tests. However, high-fidelity, predictive LES of hydrogen/air flames require models that accurately and reliably describe thermodiffusive instabilities. Present-day combustion models developed for hydrocarbon fuels, which are unaffected by such instabilities, cannot capture these effects.

To improve prediction capabilities of LES of hydrogen/air flames, detailed data of such flames are needed for model development and validation. However, for three-dimensional thermodiffusively unstable flames, only rare data exist; the available studies only qualitatively highlight the dynamics of these flames, but do not provide enough detail for quantitative model development. The high level of detail and the availability of all desired quantities at all locations motivates the use of Direct Numerical Simulations (DNS) for model development. For example, DNS provide information about reaction rates or higher-order moments, that are challenging to obtain experimentally. Recently, advances in supercomputing have enabled a range of interesting DNS studies and made DNS a powerful tool in combustion science. Within this project, a series of DNS of turbulent premixed lean hydrogen flames is conducted to generate a unique database of thermodiffusively unstable flames. From this database, LES models that account for the impact of thermodiffusive instabilities on turbulent flames can be rigorously developed.

Results and Methods

Numerical Framework

The governing equations of the DNS are given by the reacting Navier-Stokes equations in the low-Mach limit. For the computation, an in-house code called CIAO is employed. The code is a high-order, semi-implicit finite difference code that uses Crank-Nicolson time advancement and an iterative predictor corrector scheme. Spatial and temporal staggering is used to increase the accuracy. The Poisson equation for the pressure is solved by the multi-grid HYPRE solver. Momentum equations are spatially discretized with a second-order scheme. Species and temperature equations are discretized with a fifth order WENO scheme. The temperature and species equations are advanced by utilizing an operator splitting according to Strang. The chemistry operator uses a time-implicit backward difference method, as implemented in the stiff ODE solver CVODE. For further details about the applied numerical algorithms and code verification, the reader is referred to Ref. [4]. The code uses the message passing interface (MPI) standard.

Analysis of DNS database

The DNS database comprises several turbulent, lean, premixed hydrogen flames in a slot burner configuration at different conditions, where the geometry of the DNS is shown in Fig. 1. All DNS have been performed with a jet Reynolds number of 11,000 using a detailed chemical mechanism. To modulate the interactions of thermodiffusive instabilities and turbulence, three cases have been computed at different Karlovitz numbers, which parametrizes the interaction of the smallest turbulent eddies with the flame. All cases feature realistic transport models that include the differential diffusion of hydrogen, so the characteristic patterns of thermodiffusively unstable flames, such as strong variations of the heat release and super-adiabatic temperatures, are observed. Further, to systematically assess the different contributions of turbulence and thermodiffusive instabilities, an additional case has been considered for the lowest Karlovitz number using a modified diffusivity model to suppress thermodiffusive instabilities. For this, the diffusivities of all species are set equal to the thermal diffusivity (unity Lewis numbers assumption).

The significant impact of thermodiffusive instabilities on the turbulent flame dynamics is visualized in Fig. 2, where an instantaneous snapshot of the temperature field is shown for the low Karlovitz number flames with and without thermodiffusive instabilities. In the presence of such instabilities, significant super-adiabatic temperatures of up to 400 K and a much shorter flame are visible, indicating a significantly higher fuel consumption rate in the presence of instabilities. In particular, Fig. 3 shows the variation of the local heat release on the flame sheet for the low Karlovitz number flames with and without instabilities. If the instabilities are suppressed, no significant fluctuations of the local heat release are visible. In contrast, the thermodiffusively unstable flame features a strong variability of the heat release with significantly enhanced peak values compared to a laminar flame at the same conditions, leading to an overall higher fuel consumption rate. Further, the formation of tongue like structures, which are characteristic structures of thermodiffusively unstable flames, is seen. A detailed discussion of all results may be found in Berger et al. [4]“.

Ongoing Research / Outlook

The analysis of the DNS data reveals a strong impact of thermodiffusive instabilities on the dynamics of lean hydrogen/air flames. As these effects are yet not included in present combustion models, they need to be incorporated into the present LES modeling frameworks and possible model hypotheses need to be validated. For this, the present DNS represent a unique database for model development and validation. Thus, an a priori and a posteriori assessment of different premixed combustion models that are extended to account for the effects of thermodiffusive instabilities will be pursued in future work.

References and Links

[1] L. Berger, K. Kleinheinz, A.Attili, H. Pitsch Proc. Comb. Inst., 37:1879-1886, 2019. DOI:  

[2] A.J. Aspden, M.S. Day, J.B. Bell J. Fluid Mech., 680:287-320, 2011. DOI: 

[3] O. Desjardins, G. Blanquart, G. Balarac, H. Pitsch, J. Comput. Phys., 227:7125-7159, 2008. DOI: 

[4] L. Berger, A. Attili, H. Pitsch, Combust. Flame, 244:112254, 2022. DOI:


Scientific Contact 

Lukas Berger 
Institut für Technische Verbrennung
RWTH Aachen University
Templergraben 64
52056 Aachen
+49 (0)241 80-93544