**Physik | Technik**

## Jan Kamm, 2003 | Zurich, ZH

**The present work investigates circular, elliptical and swirling jet flows in the laminar Rayleigh regime. A basic equation for the free surface of inviscid circular jets is derived from Bernoulli’s principle. For the elliptical jet, a set of nonlinear partial integro-differential equations (the Cosserat equations) is derived directly from the Navier-Stokes equations, and a derivation is provided in the present work. Based on the Cosserat equations, asymptotic scaling yields an equation for the free surface of elliptical jets. Furthermore, the equations are linearized with perturbation theory and a dispersion relation is derived that yields the wavelength of elliptical jets. The phenomenon of swirling jet flows with elliptical cross-sections (water spirals) is investigated both experimentally and theoretically as the main novelty of this work. Sophisticated passive nozzles have been designed and 3D printed to reproduce the phenomenon. Experimental data is obtained for the circular, the elliptical and swirling jets and compared with theory. The results show very good agreement in general. A method to clearly distinguish the different cases is developed based on the jet wavelength.**

#### Introduction

Imposing swirl on the base flow of an elliptical liquid jet changes its physical characteristics remarkably. This phenomenon raises various research questions, in particular: (I) What are the physical effects that govern the behavior of swirling jets? (II) What are the underlying conditions that cause a jet to twist into a spiral? (III) How do the jet characteristics behave under parameter variation? These particular swirling jets have not been discussed in literature, so the present work also involved a major, experimental challenge: (IV) How can the swirling jets be reproduced to conduct accurate experimentation? To answer those questions, a thorough investigation of the more basic cases, i.e., the circular and elliptical jets, was required as well.

#### Methods

For the free surface or shape of the circular jet, a straight-forward equation is consulted from literature. For the elliptical jet, the highly complex Cosserat equations lay the foundation of the theoretical framework. With certain approximations, equations for the free surface and wavelength are established. The dynamics of swirling jets are qualitatively explained. This gives rise to a proportionality on how the wavelengths of swirling jets depend on relevant parameters. On the experimental side, a membrane pump circuit was constructed to ensure a continuous and steady flow. For the measurements, water was used. Concerning the swirling jet, sophisticated nozzles were designed and 3D printed. This allows to impose swirl on the base flow of the elliptical jet while the jet remains laminar. To support this, a CFD analysis was performed.

#### Results

For the free surface of the circular and elliptical jets, very good agreement between theory and experiments can be seen in general. This allows us to assess how certain parameters affect the system. Surface tension influences the axis-switching and dominates, together with gravity, the narrowing of the jet. Viscosity is negligible for water. For the wavelengths, we obtain again very good agreement for both the swirling and the elliptical jets. By comparing the wavelengths of the elliptical and swirling jets, we find that increasing the swirl results in a shorter wavelength of the jet. This gives rise to a clear method to distinguish the elliptical and swirling jets, which is a novelty of the present work.

#### Discussion

The results answer the initial research questions for the most part. We are able to reproduce the swirling jet with a self-developed nozzle system. Backed by empirical data, we now understand how the relevant parameters affect the system and we know the conditions under which the jet twists into a spiral. Unfortunately, investigating the effect of the orifice shape and viscosity has not been possible within this project.

#### Conclusions

With the first study on swirling jets, innovation and novelty have been achieved both on the experimental side with the nozzle development and on the theoretical front with the wavelength investigation. The work now raises the question: Are there industrial applications? This is a question that spans across various industrial fields. It is intuitive that a swirling jet could enhance mixing characteristics, which, e.g., could be applicable in polymer mixing. It would be fulfilling to tilt the first domino with this work and inspire further research on swirling jets in the coming years.

#### Würdigung durch den Experten

Prof. Dr. Daniel Weiss

Circular, elliptical and swirling free jets emanating from a nozzle are investigated in theory and experiments. Evolution equations for the development of the jet surface are developed, based on basic balance equations. A simplified model to describe the free jet surface has been developed step by step and evaluated numerically, its predictions agree well with experimental findings. Nozzles shapes have been designed and 3D printed, to reproduce experimentally the phenomena predicted. The approach applied and the project as a whole convince with their outstanding brilliance and elegance.

#### Prädikat:

hervorragend

Sonderpreis «Stockholm International Youth Science Seminar (SIYSS)» gestiftet von der Metrohm Stiftung

Sonderpreis der Schweizerischen Physikalischen Gesellschaft (SPG)

**Rämibühl-MNG, Zürich
**Lehrer: Dipl. Phys. ETH Daniel Keller