# Swirling flow in a conical diffuser generated with rotor-stator interaction

## Key Fluid Physics

The main features of the flow are the on-axis recirculation region,the vortex rope and the vortex breakdown, and wakes of the blades. The separation from the blades, flow in inter-blade passages, separation in the divergent part of the draft tube and rotor-stator interaction are among other physical mechanisms which make the flow fields complicated and difficult to model.

## Application Uncertainties

The complexity of the geometry, curved and bladed regions, tip-clearance and rotor-stator interaction, oscillation of the runner rotational speed which is absent in numerical simulations are some sources of uncertainties which make a high fidelity CFD model difficult to assemble.

## Computational Domain and Boundary Conditions

The boundary conditions also play a prominent role to reproduce the physical mechanism of the vortex breakdown. The swirl intensity determines the occurrence of the vortex breakdown. The swirl depends on the axial and tangential velocity components, which are two dominant parameters and specify the physical mechanism of the breakdown. For swirling flows in a pipe, the former determines the radius of the vortex core and the latter specifies the character of the on-axis axial velocity (jet- or wake-like). The inlet boundary condition is usually unknown at the draft tube inlet of the hydraulic turbomachines. To overcome this problem, the rotor-stator interaction, which is the interaction between the guide vane and the runner blades, is considered to retain the upstream effects on the flow in the draft tube.

## Discretisation and Grid Resolution

Most of the simulations that are available in the literature are done using licensed codes. The open source codes are normally more sensitive to the non-orthogonality of the mesh. The mesh quality is thus highly crucial in such simulations. The maximum aspect ratio of a cell is around 400 close to the outlet of the draft tube. The minimum angle is 18° for nine elements and occurs close to the hub in the runner. The computational domain contains several regions, where GGI is used at the interfaces between the regions. The resolution spacing in the normal directions to the interface should be similar at both sides of the interface. The total number of cells used in the computational domain for the high-Reynolds number models is 5.05 × 106 and for the hybrid URANS-LES models is 13.25 × 106.

## Physical Modelling

The shear layer between the two flow regions in the draft tube produces negative turbulence production [1] which makes it difficult for linear eddy-viscosity models to capture the physics of the flow. Javadi et al. [15] studied the curvature correction modeling in hydropower applications and showed that the models that are sensitive to streamline and surface curvatures perform better than the conventional eddy-viscosity models. To resolve more unsteadiness and capture the physics of the on-axis recirculation region and the vortex breakdown, higher order numerical modelling is necessary. Models which have the potential to significantly improve the flow predictions by resolving anisotropy and incorporating more sensitivity and receptivity of the underlying instabilities and unsteadiness such as second-moment closure, hybrid URANS-LES and LES are able to capture the physical mechanisms in the flow fields very well. The second-moment closure models in swirling flows are studied by the authors. These models capture the unsteadiness in the flow fields very well, although they slightly overestimate the on-axis recirculation region.

## Recommendations for Future Work

The focus of future works should be put on the control of the loss-sources in the draft tube, such as decreasing the pressure pulsations, shrinking the size of the vortex rope and the on-axis recirculation region, and even prevention of the vortex breakdown. The different control techniques should be investigated to decrease the harmful effects of the vortex breakdown and pressure pulsations [16]. The detailed simulations should be extended to a variety of geometries in hydropower such as Francis turbine, pump-turbine and Kaplan turbine. Flows under different operating conditions and with geometrical details should be studied.

## References

1. Javadi, A. and Nilsson, H.: LES and DES of strongly swirling turbulent flow through a suddenly expanding circular pipe. Comput. Fluids 107, 301-313 (2015)
2. Javadi, A. and Nilsson, H.: Time-accurate numerical simulations of swirling flow with rotor-stator interaction. Flow, Turbul. Combus. doi:10.1007/s10494-015-9632-2, (2015)
3. Bosioc, A.I., Resiga, R., Muntean, S. and Tănasă, C.: Unsteady pressure analysis of a swirling flow with vortex rope and axial water injection in a discharge cone. ASME J. Fluid Eng. 134(8), 081104, 1-11 (2012)
4. Javadi, A., Bosioc, A., Nilsson, H., Muntean, S. and Resiga, R.: Experimental and numerical investigation of the precessing helical vortex in a conical diffuser, with rotor-stator interaction. ASME J. Fluids Eng. 138(8), 081106, 1-11 (2016)
5. Resiga, R., Muntean S., Bosioc, A.I., Stuparu, A., Milos, T. and Baya, T.: Swirling flow appratus and test rig for flow control in hydraulic turbines discharge cone. 2nd IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Timisoara, Romania (2007)
6. Tănasă C., Resiga, R., Muntean, S. and Bosioc, A.: Flow-feedback method for mitigating the vortex rope in decelerated swirling flows. ASME J. Fluids Eng. 135(6), 061304, 1-11 (2013)
7. Muntean, S., Bosioc, I.A., Stanciu, R., Tănasă, C. and Resiga, R.: 3D numerical analysis of a swirling flow generator. Proc. of the 4th International Meeting on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Belgrade, Serbia, 115-125 (2011)
8. Gyllenram, W., Nilsson, H. and Davidson, L.: Large eddy simulation of turbulent swirling flow through a sudden expansion. 23rd IAHR Symposium, Yokohama (2006)
9. Javadi, A. and Nilsson, H.: LES and DES of swirling flow with rotor-stator interaction. Progress in hybrid RANS-LES modeling 130, 457-468 (2014)
10. Javadi, A., Bosioc, A., Nilsson, H., Muntean, S. and Resiga, R.: Velocity and pressure fluctuations induced by the precessing helical vortex in a conical diffuser. IOP Conf. Ser.: Earth Environ. Sci. 22, 032009 (2014)
11. Spalart, P.R., Deck, S., Shur, M.L., Squires, K.D., Strelets, M.K. and Travin, A.K.: A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comp. Fluid Dyn. 20(3), 181-195 (2006)
12. Spalart, P.R.: Detached-eddy simulation. Annu. Rev. Fluid Mech. 41, 181-202 (2009)
13. Gritskevich, M.S., Garbaruk A.V., Schütze, J. and Menter, F.L.: Development of DDES and IDDES formulations for the ${\displaystyle {k-\omega }}$ shear stress transport model. Flow. Turbulence Combust. 88, 431-449 (2012)
14. Shur, M.L., Spalart, P.R., Strelets, M.K. and Travin, A.K.: A hybrid URANS-LES approach with delayed-DES and wall-modelled LES capabilities. Int. J. Heat Fluid Fl. 29, 1638-1649 (2008)
15. Javadi, A., Krane, E. and Nilsson, H.: Exploration of rotation/curvature correction method in hydropower application. Turbulence, Heat and Mass Transfer 8, Sarajevo, Bosnia and Herzegovina. (2015)
16. Javadi, A. and Nilsson, H.: Active flow control of vortex Rope in a conical diffuser. IAHR WG Meeting on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Ljubljana. (2015)
17. Bosioc, A., Susan-Resiga, R. and Muntean, S.: Design and Manufacturing of a Convergent-Divergent Test Section for Swirling Flow Apparatus. Proc. 4th German-Romanian Workshop on Turbomachinery Hydrodynamics, (Stuttgart, Germany) June 12-15, 1 -15 (2008)
18. Resiga, R., Muntean, S., Tanasa, C. and Bosioc, A.: Hydrodynamic Design and Analysis of a Swirling Flow Generator. Proc. 4th German - Romanian Workshop on Turbomachinery Hydrodynamics (Stuttgart, Germany) June 12-15, 1-16 (2008)
19. Resiga, R, Muntean, S and Bosioc, A.: Blade Design for Swirling Flow Generator. Proc. 4th German - Romanian Workshop on Turbomachinery Hydrodynamics (Stuttgart, Germany) June 12-15, 1-14 (2008)
20. Resiga, R. and Muntean, S.: Decelerated Swirling Flow Control in the Discharge Cone of Francis Turbines. Proc. 4th Symp. on Fluid Machinery and Fluid Engineering (Beijing, China) 4ISFMFE-IL18, 89-96 (2008)

Contributed by: A. Javadia, A. Bosiocb, H Nilssona, S. Munteanc, R. Susan-Resigab — aChalmers University of Technology, Göteborg, Sweden; bUniversity Polytehnica Timişoara, Timişoara, Romania; cCenter for Advanced Research in Engineering Sciences, Romanian Academy, Timişoara Branch, Timişoara, Romania