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Rotating flow systems are often used to study stability phenomena and structure developments. The closed spherical gap problem is generalized into an open flow system by superimposing a mass flux in meridional direction. The basic solutions at low Reynolds numbers are described by analytical methods. The nonlinear supercritical solutions are simulated numerically and realized in experiments. Novel steady and time-dependent modes of flows are obtained. The extensive results concern the stability behaviour, non-uniqueness of supercritical solutions, symmetry behaviour and transitions between steady and time-dependent solutions. The experimental investigations concern the visualization of the various instabilities and the quatitative description of the flow structures including the laminar-turbulent transition. A comparison between theoretical and experimental results shows good agreement within the limit of rotational symmetric solutions from the theory.
This study focuses on the experimental and numerical investigations on a commercial Ranque-Hilsch vortex tube. Ranque-Hilsch vortex tubes have many applications in industry and production as they can generate a very cold flow just from pressurized air .e.g. machine tool cooling. Main objective of this study is the energy separation in the flow field which results in a temperature drop on the cold exit of the tube. This was investigated experimentally by measuring the outlet temperature on the cold exit and the pressure drop on the flow restrictor valve on the hot exit. At a pressure drop of 0.5 bar the vortex tube showed the best performance by reaching a cold exit temperature of –16.7 °C. The Inlet flow was pressurised air at 20 °C and 6 bar.<br /> The numerical analysis was carried out by full 3D steady state CFD-simulation using the commercial software ANSYS CFX 11.0. The three dimensional model represented a 120° sector of the tube using periodic boundary conditions. A comparison between different turbulence models (k – å, RNG k – å, k – ù, SST) was carried out. The classic k – å two layer turbulence model showed the best results compared to the experiment. The energy separation and the drop in cold exit temperature are highest when the viscous work term is included into the energy equation. These effects of including the viscous work term into the energy separation have also been investigated.
Jürgen Zierep passed away on July 29, 2021, at the age of 92. To him, science and education was not only a profession, but an affair of the heart. His impressive contributions in fluid mechanics comprise about 200 scientific publications in the fields of gas dynamics, similarity laws, flow instabilities, flows with energy transfer, and non-Newtonian fluids. In addition, he wrote eleven textbooks with great dedication. Those books by the “scientist who loves to teach” are nowadays available in different languages and regularly appear in new editions.
The structure of the separation bubble that appears in the secondary meridional flow between two coaxially rotating spheres at low and finite Reynolds number (Re) is considered. The low Re analytical study was motivated by recognizing some errors in the analytical work on this problem by Arunachalam and Majhi (1987, Q. Jl Mech. Appl. Math., 40, 47) whilst the finite Re experimental study was motivated by the desire to observe the separation bubble in the laboratory. Though the finite Re experiments were performed in a confined apparatus, they exhibit the qualitative features of the low Re theoretical predictions for the axisymmetric separation bubble that encloses two toroidal vortices symmetrically disposed above and below the mid‐plane of sphere separation, but strong effects of confinement are apparent. The flows observed include (i) a wall‐attached bubble symmetric about the mid‐plane at low Re, (ii) symmetric free‐standing bubbles at moderate Re, and (iii) an asymmetric bubble with flow separating from one sphere and attaching to the support shaft between the spheres at sufficiently high Re.
Flows in nature and technology are often associated with specific structures and pattern. This paper deals with the development and behaviour of such flow pattern. Flow structures are important for the mass, momentum and energy transport. The behaviour of different flow pattern is used by engineers to obtain an efficient mass and energy consumption. Mechanical power is transmitted via the momentum of rotating machine parts. Therefore the physical and mathematical knowledge of these basic concepts is important. Theoretical and experimental investigations of principle experiments are described in the following. We start with the classical problem of the flow between two concentric cylinders where the inner cylinder rotates. Periodic instabilities occur which are called Taylor vortices. The analogy between the cylindrical gap flow, the heat transfer in a horizontal fluid layer exposed to the gravity field and the boundary layer flow along concave boundaries concerning their stability behaviour is addressed. The vortex breakdown phenomenon in a cylinder with rotating cover is also described. A generalization to spherical sectors leads then to investigations with different boundary conditions. The spherical gap flow exhibits interesting phenomena concerning the nonlinear character of the Navier-Stokes equations. Multiple solutions in the nonlinear regime give rise to different routes during the laminar-turbulent transition. The interaction of two rotating spheres results in flow structures with separation and stagnation lines. Experimental results are confirmed by numerical simulations.
This mature textbook brings the fundamentals of fluid mechanics in a concise and mathematically understandable presentation. In the current edition, a section on dissipation and viscous potential flows has been added. Exercises with solutions help to apply the material correctly and promote understanding.
The free convection in a vertical gap is generalized to realize new analytical solutions of the Boussinesq-equations. The steady and time-dependent solutions for the temperature and velocity distribution are discussed in detail depending on the mass flux in vertical direction. The range of existence for flows with and without back flow is obtained. The transient behaviour of the solutions during the time-dependent development displays interesting physical behaviour.