# An analytical and experimental investigation of flow characteristics generated by rotating porous disk

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## Abstract

This paper is concerned with investigations of the gas flow around and in the cell-porous rotating disk. A simple 1D model of gas flow is presented. Usually the cell-porous materials are applied in heat exchangers and stationary filters. On the other hand, peculiarities of the flow revealed under theoretical analysis and some experimental observations demonstrate that rotating porous disks may also be effectively exploited in the shear-force machines for the gas transport purposes.

## Keywords

Cell-porous materials Filtrational hydrodynamics Gas flow in rotating system Shear-force pumps Heat exchangers## Nomenclature

*d*Porous disk width

*k*Drag force coefficient

*p*Pressure

- \(P = \frac{{p - p_{\infty}}}{{\rho \omega ^{2} R^{2}_{0}}}\)
Non-dimensional pressure

*q*Gas flow rate through the disk

- \(Q = \frac{q}{{\omega R^{2}_{0}}}\)
Non-dimensional gas flow rate through the disk

- \(\vec{r}\)
Radius vector

- \({\left| {\vec{r}} \right|} = r\)
Radius in cylindrical coordinates

*R*_{0}Radius of the porous disk

*u*Tangential component of the gas velocity

- \(U = \frac{u}{{\omega R_{0}}}\)
Non-dimensional tangential component of the gas velocity

- \(\vec{V} = (v, u, w)\)
Vector of the gas velocity

*v*Radial component of the gas velocity

- \(V = \frac{v}{{\omega R_{0}}}\)
Non-dimensional radial component of the gas velocity

- w
Axial component of the gas velocity;

- \(W = \frac{w}{{\omega R_{0}}}\)
Non-dimensional axial component of the gas velocity

*z*Axial coordinate

## Greek symbols

- δ=
*d*/*R*_{0} Small non-dimensional parameter (ratio between disk width and disk radius)

- κ=
*kR*_{0} Non-dimensional drag force coefficient

- ρ
Gas density

- \(\varsigma = \frac{r}{{R_{0}}}\)
Non-dimensional radial coordinate

- ω
Angular velocity of the gas rotation

## Notes

### Acknowledgements

The authors are grateful to Mr. D. V. Chusov and Mr. A. D. Frolov for technical advice and Mr. A. Ya. Korotkih for his help in experiments. This work was partially supported by the Siberian Branch of Russian Academy of Sciences under the integration project entitled “Flows generated by cell-porous rotors and their application in energy conversion devices”.

## References

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