The modelling of turbulent combustion of ammonia is particularly challenging due to the complex chemistry featuring an exceptionally wide range of primary chemical time-scales demanding accurate inclusion of turbulence–chemistry interactions. The latter are here treated using a transported joint-scalar probability density function method that enables direct inclusion, without simplification, of a comprehensively validated H/N/O mechanism. The approach is used to model two turbulent ammonia/hydrogen/nitrogen flames at a pressure of 5 atm and at a Reynolds number of 11,200. The use of hydrogen rich mixtures at low Reynolds numbers, together with increased scalar gradients at elevated pressures, raises the issue of differential diffusion, which is included through a decomposition of the terms for molecular transport in composition space and molecular transport in physical space. The latter, which is often neglected under high-Reynolds-number assumptions, is included, while molecular transport in composition space is treated using the Euclidean Minimum Spanning Tree and Modified Curl’s models. The current approach provides good overall agreement with experimental data for both mean and root-mean-square values. The inclusion of molecular transport in physical space produces modest, but consistent, improvements in hydrogen statistics, especially downstream where turbulence has decayed. By contrast, the application to a turbulent hydrogen diffusion flame shows a substantial impact. These findings clarify the role of molecular transport in turbulent flames featuring high hydrogen concentrations. Novelty and significance statement Current transported joint-scalar probability density function (JPDF) methods normally neglect molecular transport in physical space (MTPS) by invoking high-Reynolds-number assumptions, limiting their ability to represent differential diffusion. The limitation is of particular concern for turbulent cracked-ammonia flames at elevated pressures, where local scalar gradients are enhanced and slow ammonia oxidation coexists with fast hydrogen chemistry. This work establishes the first JPDF-MTPS treatment of such flames and further demonstrates the importance of retaining locality in composition space for micromixing models. Its significance also lies in identifying the contribution of differential diffusion in regions of strong scalar gradients and reduced turbulence, rather than being limited to near-field burner regions as previously reported. It is further shown that the impact increases with hydrogen concentration through the application of JPDF-MTPS to a turbulent non-premixed hydrogen flame.
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