Modal decompositions are a great tool to automatically identify and separate different features & phenomena in a flow. They can be used for many useful things:
- Give us a better understanding by separating flows into their different modes.
- Reconstruct the flow using just the dominant modes with major flow features and thereby filter away measurement noise and outliers, typically described by the higher order modes.
- Be used for data reduction by storing just the dominant modes with the highest energy content and later reconstruct the flow from the stored data.
Modal decompositions can also be used for stability analysis when Oscillating Pattern Decomposition, identify cyclic patterns in the flow along with frequencies and growth or decay rates. DynamicStudio features two main families of Decompositions.
The first are based around the well known Proper Orthogonal decomposition, which is part of the base package. The derivatives of the POD are included in the Advanced Modal Decomposition Add-on.
The second category is the Oscillating Pattern Decomposition (OPD) Add-on, which is more used for stability analysis.
In total, five different decomposition methods help you to find the perfect match for your data:
- Proper Orthogonal Decomposition (POD)
- Multiscale POD (mPOD)
- Fourier Modal Decomposition (FMD)
- Spectral POD (sPOD)
- Oscillating Pattern Decomposition (OPD)
Proper Orthogonal Decomposition (POD)
The classic Modal decomposition in DynamicStudio is the POD. As with all modal decompositions, it separates the flow into different modes in both space (Topos) and time (Chronos). Each of these modes represents a certain type of flow feature like a vortex, for example. The modes are sorted by energy content with mode 0, the mean, first, followed by less and less energetic modes.
Advanced Decompositions
All the advanced decompositions are specifically intended for time resolved data, where the content of one snapshot correlates with at least 10 consecutive data sets. The goal of the different decompositions is to find self similarities of different modes or structures in the frequency domain.
That works very visually on the covariance matrix. This matrix is supposed to show the frequency content of a mode on the main diagonal. If it has multiple peaks, this will generate cross-talk of frequencies between the different modes.
In order to suppress this cross-talk, the additional methods like the sPOD, mPOD and FMD have been designed. The image below describes this quite well on the example of a pulsating jet flow measured with a VV system.
Multiscale Proper Orthogonal Decomposition (mPOD)
The mPOD collaboration with the von Karman Institute, Belgium (VKI) published in Measurement Science and Technology won the publication’s Outstanding Paper Award for 2020 in the field of Fluid Mechanics.
The idea is to apply a filter around the peaks in the covariance matrix, and treat each of these blocks separately to avoid cross talk of the frequencies between the modes. To establish these filters, the UI gives you some guidance and it is as simple as dragging and dropping the frequency borders of the blocks.
Fourier Mode Decomposition (FMD)
Taking the approach of the mPOD, the FMD completely separates the modes by their frequency content, by adding as many filters along the main diagonal as there are modes. Thus, all modes are frequency independent from each other, which is a great tool if you want to study the influence of e.g. shedding frequencies or impinging jets, where many different vortical structures are present, but with different frequencies.
The main differences of the different modal decomposition methods offered in DynamicStudio can be seen in the comparison figure 2: the plots of the Chronos and the spectrum of a mode. Here, in the 3rd row, for FMD the spectrum of the mode is just vertical lines.
Spectral Proper Orthogonal Decomposition (sPOD)
By combining the ideas of the mPOD and the FMD with a gradient in between to not strictly separate each frequencies from each other, the sPOD (Based on M. Sieber et al 2016) allows a gradual fall-off when filtering the main diagonal. The intensity of this filter drop can be adjusted manually to avoid cross-talk of a few main modes, yet still allow a bit of the frequency content to interact on different modes.
Oscillating Pattern Decomposition (OPD)
With Classic POD Analysis as preprocessing of a time-resolved dataset, OPD performs stability analysis of the flow. Resulting modes have distinct frequencies plus exponential growth or decay rates to identify dominant flow structures. OPD Topos are complex and can be animated to visualize features such as traveling vortices in the flow. This add-on is ideal for investigating vortex shedding in shear regions, acoustic- or thermo-acoustic driven vortex formation, and vortex enhancement. A key reason for investing in a TR-PIV system is the ability to perform frequency domain analysis. OPD software is a dedicated tool for such analysis and therefore an indispensable complement to any TR-PIV system.
