Klingl, Stefan; Lecheler, Stefan; Pfitzner, Michael. (2024). Direct numerical simulation of laminar, transitional and turbulent radially inward flow between closely spaced corotating disks. European Journal of Mechanics / B Fluids, Vol. 105, S. 119-137.


This study describes direct numerical simulation (DNS) of radially inward spiralling corotating disk flow with a narrow disk spacing, using the open source solver Nek5000 and the supercomputer SuperMUC-NG at Leibniz Supercomputing Centre. Knowledge about laminar and turbulent regime boundaries in this flow scenario is important for modelling and performance prediction of friction turbines. Simulations are performed in differently sized sections of the flat annulus that is formed by two opposing corotating disk surfaces. Three sets of operating conditions are covered, from the laminar, transitional and turbulent region of a previously determined stability chart respectively. Directly downstream of the inlet boundary, the flow is artificially perturbed with a random body force acting normal to the disk surfaces. Fourier analysis of the DNS flow field reveals that the artificial perturbation is dampened across all wavenumbers for the laminar conditions, while at the transitional conditions a small range of modes is weakly amplified towards the outlet. The identified unstable modes were previously correctly predicted by linear stability analysis. Comparison to experimental velocity profile measurements from a previous study at the same transitional operating conditions suggests strongly perturbed flow during the experiment. For inflow conditions leading to turbulent flow, average velocity profiles from DNS coincide with those from experiment and from commercial fluid simulation software with turbulence modelling (ANSYS CFX). Close to the walls, turbulent dissipation and turbulent kinetic energy distributions do not agree with the ANSYS CFX results. Friction Reynolds number settles at about 118 after turbulent flow has developed from the initial perturbation. Two point correlations and corresponding energy spectra are presented.  





Klingl, Stefan; Lecheler, Stefan; Pfitzner, Michael. (2022). Absolute and convective stability of flow between closely spaced co-rotating disks with imposed throughflow. European Journal of Mechanics / B Fluids, Vol. 91, S. 226-232.


Different types of rotating disk boundary layers were previously shown to be absolutely unstable. The present study checks if this is also true for the flow between narrowly spaced co-rotating disks with merged boundary layers and imposed throughflow. The described method is able to reproduce the absolute instability of the von Kármán boundary layer and of radially outward flow between co-rotating disks with separated boundary layers. Nevertheless, no absolute instability is found for the case of narrow disk spacing with merged boundary layers for both radially inward and outward flow. The data does however show convective instability. Stability maps are provided for the analyzed parameter space.  





Klingl, Stefan; Lecheler, Stefan; Pfitzner, Michael. (2020). Linear stability investigations on the inward flow between closely spaced co-rotating disks. European Journal of Mechanics. B, Fluids, Vol. 84, S. 455-469.


In order to identify transitional flow, the linear stability of inward flow in a narrow gap between co-rotating disks is studied. Two methods are developed. The local approach assumes periodic nature of the flow in radial and circumferential direction, whereas the computationally more expensive biglobal variant only requires periodicity in circumferential direction. Stability maps are provided for a single set of operating conditions spanning a range of Reynolds numbers at fixed rotor geometry and rotational speed. The theoretical findings are compared to a set of experimental velocity profiles that includes the transitional region according to profile shapes. Apart from some explainable inconsistencies, the determined stability limits agree with each other and with results from previous studies.





Klingl, Stefan; Lecheler, Stefan; Pfitzner, Michael. (2019). Experimental, numerical and theoretical investigations of Tesla turbines. Sustainable Polyenergy Generation and Harvesting Conference ans Exhibition (2019, Savona).


We use analytical, numerical and experimental methods to characterize the laminar flow inside a Tesla turbine rotor gap. A comparison based on one particular set of operating conditions mutually validates the three approaches. The simplicity of the analytical flow model allows for a cost efficient optimization of the underlying turbine parameters. Performance charts exhibit general trends and serve as a guide for preliminary turbine design and optimization. In terms of the ratio of half the gap width to inlet radius and the ratio of outlet- to inlet radius, the designer of a tesla turbine has to find a compromise between optimal efficiency and optimal power output.


Schosser, Constantin; Klingl, Stefan; Lecheler, Stefan; Fuchs, Thomas; Hain, Rainer; Kähler, Christian J.; Pfitzner, Michael. (2019). Comprehensive investigation of the flow in a narrow gap between co-rotating disks. European Journal of Mechanics - B/Fluids, Vol. 78, S. 50-61.


The inward flow between two parallel, co-rotating disks undergoes a thorough examination by analytical, experimental and numerical means. The analytical approach utilizes the asymptotical truncated series solution provided by Batista (2011) and extends it by a correction for an arbitrary mean tangential velocity at the rotor inlet. Taylor series expansions of the analytical results provide an estimate for the orders of magnitude of velocity components and the polynomial order of their profile shapes. The common assumption of parabolic velocity distributions is only appropriate in the radial direction. In parallel, a unique test rig provides the experimental counterpart of the velocity profiles inside a rotor gap, that is suitably narrow for turbomachinery applications. The optical flow measurements are based on a novel calibration technique and volumetric particle tracking evaluation. Both laminar and turbulent operating conditions are examined. Finally, numerical studies using commercial CFD software provide insight into the flow field inside the test rig rotor where experimental methods fall short and provide an additional means to investigate the effects of the approximations made in the derivation of the analytical results. The velocity distributions acquired by analytical, numerical and experimental means agree well, the asymptotical nature of the analytical solution by Batista (2011) can be observed. The comparison of experimental and numerical results of a turbulent case suggests that the Shear Stress Transport turbulence model reproduces turbulent flow inside the rotor gap appropriately.





Lecheler, Stefan. (2018). Schneller Einstieg in ANSYS CFX 18 durch einfache Beispiele. Springer Vieweg (4.Ed.).




Schosser, Constantin; Fuchs, Thomas; Hain, Rainer; Lecheler, Stefan; Kähler, Christian J. (2016). Three-dimensional particle tracking velocimetry in a Tesla turbine rotor using a non-intrusive calibration method. International Symposium on Applications of Laser Techniques to Fluid Mechanics (18., 2016, Lissabon).

Lecheler, Stefan. (2016). Amortisation Time Estimation of Newly Planned Geothermal Heat and Power Plants. Low Carbon Green Growth Earth Summit (6., 2016, Goyang City).


Lecheler, Stefan (2014). Numerische Strömungsberechnung: Schneller Einstieg durch anschauliche Beispiele mit ANSYS15.0 (3.Ed.). Springer Viehweg.



Schosser, Constantin; Lecheler, Stefan; Pfitzner, Michael. (2014). A Test Rig for the Investigation of the Performance and Flow Field of Tesla Friction Turbines. Proceedings of ASME Turbo Expo 2014: Turbine Technical Conference and Exposition GT2014 June 16 – 20, 2014, Düsseldorf, Germany, S.1-11.


The paper summarizes the development and optimization of a flexible test facility for 3D tomographic PIV/PTV measurements of the flow field in the rotor gap of a Tesla friction turbine and performance evaluations. The main aim of the experiment will be the validation of CFD simulations. Another intention is to gain a deeper understanding of the flow phenomena in the gap. The extension of existing theoretical investigations lead to an improved knowledge of dimensioning such bladeless turbines with the goal of maximum power and efficiency. The mechanical design of the rotor, based on these equations, was optimized for a minimal deformation and low mechanical stress. Modal and harmonic response analyses due to imbalance forces have been performed to ensure low vibrations during operation. The design of the feed and guide vanes have been optimized for uniformity of the flow entering the Tesla disk’s gap. The rotor outlet is optimized to achieve minimal pressure loss at the intended exit swirl angle. For the demonstration of the measurement technique preliminary tomographic PIV/PTV tests have been carried out. The measurement, safety monitoring and feedback-control software was developed for running on a National Instruments compact RIO real-time target.





Lecheler, Stefan (2013). A Program for First Estimation of Power Output, Costs and Profit for Geothermal Heat and Power Plants. International Seminar on ORC Power Systems (2., 2013, Rotterdam).