# Pulsating duct flow

###### tags: `documentation`

## Velocity field analysis methodology

Following [Mohseni et al., JFM 2001](https://www.cambridge.org/core/services/aop-cambridge-core/content/view/64713CBC523988BC8EDEB9A5155EBCB2/S0022112000003025a.pdf/numerical-experiments-on-vortex-ring-formation.pdf), who present a numerical investigation of vortex ring formation, we will analyse the vortex trajectory. The corresponding figure from the paper is below.
**Q**: Which vortex to track and how to obtain the vortex center?


We will also plot the evolution of the vorticity field via streamlines as in Fig. 3 of the paper. The plot from the paper is given below.


This should be a rather straightforward exercise and can be obtained **first**.

Also the circulation will be plotted as a function of time.
**Q**: Define circulation in Matlab.

[Dabiri and Gharib, JFM 2005](https://www.cambridge.org/core/services/aop-cambridge-core/content/view/CD7BF388CF2398D73505ADDBB5F896CA/S002211200500515Xa.pdf/starting-flow-through-nozzles-with-temporally-variable-exit-diameter.pdf) have also analysed the starting jet in experiments with time-varying jet exit nozzle.
> [name=asaurabh] What results from the paper did you want to use?

In [Nitsche and Krasny, JFM 2006](https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/abs/numerical-study-of-vortex-ring-formation-at-the-edge-of-a-circular-tube/CDC7D2307CDBA04124BA05884FA46948) results of the numerical modeling of experiments reported in [Didden 1979](https://link.springer.com/content/pdf/10.1007/BF01597484.pdf) are presented. Characteristic vortex formation from the experiments are shown below:


> [name=asaurabh] Which results from Nitsche et al. and Didden did you want to pursue?

> [name=asaurabh] I found a poster from John Baker's group (Minnesota): [Visualization of pulsating low speed flows from a basic annular jet](https://conservancy.umn.edu/bitstream/handle/11299/58934/Padron_Showcase2009_Poster.pdf;sequence=1). See if you can find corresponding papers. This could be close to validation and selection of forcing parameters.

A similar numerical investigation by [Chang et al., 2018](https://www.sciencedirect.com/science/article/pii/S2214157X18302077) reported the effect of a periodic forcing imposed on the jet in the case of a low speed jet-in-crossflow configuration.

> [name=asaurabh] Note that the study is very simplistic straightforward report with not much insight---at least when I browsed. Nonetheless, such a report should be your first effort. You can improve subsequently.

## Task to do in order to complete the paper
- [ ] Validation
- [ ] Grid Independence(If the higher number of grids shows result deviation from the lower number of grids then we have to perform simulation again with hugher number of grids)
- [ ] Domain Independence(In this we have to show that the length of larger channel which we have taken[60 Di] is optimum and if we increase that result remain unaffected)
- [ ] Analysis of result