Proper orthogonal decomposition and dynamic mode decomposition of jet in channel crossflow

Highlights: • POD and DMD was applied on the DNS snapshots of jet in channel crossflow. • The sensitivity of POD/DMD analysis was studied. • Low-order reconstructions were analysed with four different DMD approaches. • POD/DMD results are linked with instability mechanisms. - Abstract: The paper is devoted to the application of the model order reduction to the results of direct numerical simulation of a low momentum laminar jet discharged into a laminar channel crossflow through a circular orifice (Reynolds number $\mathrm{Re}=3333$, jet-to-crossflow velocity ratio is $R=1/6$, mesh 13 million nodes, (Wu et al., 2017a)). Main attention is paid to the post-processor analysis of the computational results via model order reduction techniques: the Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) which can drastically reduce the amount of data needed. Up to 400 snapshots, obtained by direct numerical simulation, are used to extract the structures. We study the sensitivity of both algorithms to the sampling frequency and time span. For the first time different DMD ranking approaches are analysed in the application to a low-dimensional flow reconstruction. It is shown that the DMD approach with the ranking with respect to the amplitudes averaged over time is the most efficient technique for the problem in study. A comparative analysis is also carried out for both POD and DMD. It is shown the energy is more evenly distributed in the DMD. In turn, the POD is quite optimal in reconstructing the flow while the DMD requires more modes to capture the same amount of energy. However, DMD modes automatically reveal the frequency information and corresponding spatial structures in the entire field as well as interactions between different parts of the flow domain.