Physics-informed machine-learning (PIML) enables the integration of domain knowledge with machine learning (ML) algorithms, which results in higher data efficiency and more stable predictions. This provides opportunities for augmenting—and even replacing—high-fidelity numerical simulations of complex turbulent flows, which are often expensive due to the requirement of high temporal and spatial resolution. In this review, we (i) provide an introduction and historical perspective of ML methods, in particular neural networks (NN), (ii) examine existing PIML applications to fluid mechanics problems, especially in complex high Reynolds number flows, (iii) demonstrate the utility of PIML techniques through a case study, and (iv) discuss the challenges and opportunities of developing PIML for fluid mechanics.

The study of stoichiometric flame lengths of laminar jet or co-flow diffusion flames has been a major topic of research in last few decades, mostly focusing on flames of either undiluted or slightly diluted fuel reacting with air. However, the flame characteristics under extremely diluted fuel conditions are not well studied. Hence, a set of experiments and numerical simulations have been performed in the present work to study the flame lengths for a wide range of fuel and oxidizer dilutions using two different jet diameter burners (4 and 9 mm with identical volume flow rates). Both experimental and numerical results confirm that the 4 mm burner flame length is consistently higher than the 9 mm burner counterpart. This difference is attributed to the higher temperature of the 9 mm burner flame, which in turn is due to its lower conductive heat loss to the ambient. Several analytical models, available in the literature to predict the flame lengths, such as Roper, Li-Gordon-Williams (LGW), and Wang-Sunderland-Axelbaum (WSA), have also been analyzed and compared with the experimental data. A new analytical model is also proposed in this study by modifying the species diffusivity and flame temperature in WSA model. This revised model predicts the flame lengths better than the other analytical models, especially when the fuel stream is diluted.