We revisit the classical problem of flow of electrolyte solutions through charged capillary nanopores or nanotubes as described by the capillary pore model (also called "space charge" theory). This theory assumes very long and thin pores and uses a one-dimensional flux-force formalism which relates fluxes (electrical current, salt flux, and fluid velocity) and driving forces (difference in electric potential, salt concentration, and pressure). We analyze the general case with overlapping electric double layers in the pore and a nonzero axial salt concentration gradient. The 3×3 matrix relating these quantities exhibits Onsager symmetry and we report a significant new simplification for the diagonal element relating axial salt flux to the gradient in chemical potential. We prove that Onsager symmetry is preserved under changes of variables, which we illustrate by transformation to a different flux-force matrix given by Gross and Osterle [J. Chem. Phys. 49, 228 (1968)]. The capillary pore model is well suited to describe the nonlinear response of charged membranes or nanofluidic devices for electrokinetic energy conversion and water desalination, as long as the transverse ion profiles remain in local quasiequilibrium. As an example, we evaluate electrical power production from a salt concentration difference by reverse electrodialysis, using an efficiency versus power diagram. We show that since the capillary pore model allows for axial gradients in salt concentration, partial loops in current, salt flux, or fluid flow can develop in the pore. Predictions for macroscopic transport properties using a reduced model, where the potential and concentration are assumed to be invariant with radial coordinate ("uniform potential" or "fine capillary pore" model), are close to results of the full model.

Although turbines are commonly noted for their high efficiency this efficiency can be improved further. The importance of the leakage flow for the losses of turbine stages makes this flow a promising candidate to be examined for loss reduction: first it decreases the workflow through the rotor and second, the suction side incidence of the re-entering leakage flow in the subsequent stator causes additional losses. As an essential parameter for leakage flow the clearance and its influence on the losses is investigated by experimental and numerical approach as well. The measurements of the experimental part were carried out on a 1.5 stage axial model turbine of an enlarged scale. The rotor of the turbine consists of shrouded blades with two teeth on the shroud. The clearance was varied from s/D = 0.0007 up to 0.004. Linear traverse measurements with a pneumatic 5-hole probe were taken in front of and behind the second stator. The re-entering leakage flow extremely influences the flow properties in radial direction (up to 50% of the span) at the inlet of the following stator. So the flow angle α1 deviates up to 90° of the flow angle in the mid-span, depending on the clearance. Along with mixing losses, this suction side incidence leads to an increase of the losses within the stator. In addition numerical investigations of the flow field were done with the commercial flow solver CFX-TASCflow. The interaction between the leakage flow and the secondary losses of the following stator is shown, and a comparison with available loss correlations is carried out in this paper.

This paper presents the results of an experimental investigation into the flow in a 1.5-stage low-speed axial turbine with a straight labyrinth seal on the rotor shroud. The paper focuses on the interaction between the leakage flow and the main flow. The experimental program consists of measurements of the three-dimensional properties of the main flow downstream of the rotor trailing edge after the re-injection of the leakage flow. The measurements were carried out using pneumatic five-hole probes and three dimensional hot-wire probes at different operating points of the turbine. The measurement plane behind the rotor extends over one pitch from the shroud to the casing, with the complex three-dimensional flow field being mapped in great detail by 1,008 measurement points. As demonstrated in this paper, the entering leakage flow not only introduces mixing losses but also predominates the secondary flow behind the rotor and the second stator. The experimental data show that even at realistic clearance heights the leakage flow gives rise to negative incidence of considerable parts of the downstream stator which causes the flow to separate. Thus, labyrinth seal leakage flow should be taken properly into account in the design or optimisation process of turbomachinery. The high number of measurement points allows detailed analysis of the secondary flow phenomena and of the vortex structures. The time-dependence of the position and the intensity of the vortices is shown and the influence of the turbine’s operating point is presented.

This paper provides an investigation of a casing treatment (CT) approach for pressure ratio improvements of centrifugal compressors between peak efficiency and surge. Results were experimentally verified for a variety of automotive turbocharger compressors and analyzed with 3D CFD. The CT design is an adaptation from an axial high-pressure compressor, which was successfully applied and intensively investigated in recent years. The aerodynamic working principle of the applied CT design and the achievable improvements are shown and described. The demand of operating range for automotive applications typically dictates high inlet shroud to outlet radius ratio (high trim) and past experiences indicate that a recirculation zone is formed in the inducer for those centrifugal compressors. This recirculation at the inlet shroud causes losses, a massive blockage and induces a co-rotating swirl at the inlet of the impeller. The result is a reduced pressure ratio, often leading to flat speed lines between the onset of recirculation and surge. This paper provides an understanding of inducer recirculation, its impacts and suggests countermeasures. The CT design for centrifugal compressors only influences flow locally at the inducer and prevents recirculation. It differs substantially in design and functionality from the classical bleed slot system commonly used to increase operating range. An experimental and CFD comparison between these designs is presented. While the classical bleed slot system often provides a massive increase in operating range, it often fails to increase the pressure ratio between onset of inducer recirculation and surge. In contrast, the CT design achieves a gain in pressure ratio near surge.