We discuss (i) the measurement, (ii) interpretation and (iii) technical impact of temperature-dependent wall slip and its activation energy for polar and non-polar hydrocarbon Newtonian fluids moving relative to machined metal surfaces. A newly developed apparatus, the slip length tribometer (SLT), overcomes the drawbacks of existing measurement devices in terms of characterising relevant rough surfaces by measuring the slip length at different temperatures over a sufficiently large wetted area. The experimental data show that the bulk viscosity and slip length at the fluid–metal interface is independent of the shear rate up to $10^5\,\mathrm {s}^{-1}$ , being consistent with recent results from molecular dynamics simulations by Mehrnia & Pelz (J. Mol. Liq., vol. 336, 2021, 116589). Furthermore, the activation energies for wall slip and bulk shear determined by means of the SLT differ by a factor of two, i.e. $E_{\lambda }\approx 0.5 E_\mu$ for non-polar hydrocarbon molecules sliding relative to metal walls. This difference is explained by a generalised Eyring model applied to wall slip. The paper closes with the impact of wall slip on Sommerfeld's similarity theory of tribology and the resulting Stribeck curve (Sommerfeld, Z. Math. Phys., vol. 50, 1904, pp. 97–155; Z. Tech. Phys., vol. 2. Jahrg., 1921; Mechanik der deformierbaren Medien, 1944, Akademische Verlagsgesellschaft Becker & Erler). For this purpose, Reynolds’ equation generalised for wall slip is solved in combination with the experimentally determined constitutive relations for bulk shear and wall slip to predict typical characteristics of journal bearings. The results show that, for a typical journal bearing, where the ratio of slip length to average bearing clearance is of the order of $10^{-2}$ , the influence of wall slip on both load-carrying capacity and dissipation is not negligible. This work combines nanofluidics and tribology in order to provide methods and knowledge for e.g. tailor-made fluids and interfaces.
The performance and reliability of turbomachinery is often limited by shaft vibrations induced by fluid forces of (i) plain or profiled annular seals, (ii) pistons and (iii) journal bearings. The rotordynamic coefficients namely, stiffness, damping and inertia of plain annular seals are in general calculated using the bulk-flow approach developed by Childs. However, when applying the calculation method to profiled gaps, especially those with non-symmetrical profiles, large differences between simulation and experimental data are reported. Furthermore, reliable experimental data as well as large databases including experimental and simulation results from a single author are limited. To overcome this, the paper introduces a unique active magnetic bearing test rig, built and operated at the Technische Universität Darmstadt as well as the corresponding simulation method to determine the rotordynamic influence of annular seals. An extensive experimental study is carried out investigating plain, symmetrically profiled and non-symmetrically profiled annular seals within the relevant parameter range for turbulent flow in pumps. The results are compared to the simulation results showing a significant influence of profiled gaps on the dynamic characteristics in comparison to plain annular seals. Furthermore, it is shown that symmetric and non-symmetric profiles have a different influence on the dynamic quantities inertia, damping and stiffness.
Nowadays, most studies of the dynamic characteristics of annular gaps focus only on the force characteristics due to translational motions, while the tilt and moment coefficients are less well studied. To expand the knowledge of the additional coefficients, we investigate both the dynamic force and the dynamic and moment characteristics of annular gaps. First, the rotordynamic influence of annular gaps is recapitulated. Second, a new simulation method is presented, using a perturbed integro-differential approach in combination with a Hirs' model and power-law ansatz functions for the velocity profiles to calculate the dynamic force and moment characteristics. Subsequently, an extensive parameter study is carried out. To evaluate whether the hydraulic tilt and moment coefficients need to be considered, an effective stiffness is defined and the influence of the annulus length, an eccentrically operated shaft, the centre of rotation, a modified Reynolds number, the flow number and the pre-swirl is investigated. It is shown that despite the annulus length, the flow number as well a modified Reynolds number are crucial for the relevance of the additional coefficients. This leads to a simple three-dimensional diagram, which makes it possible to assess the necessity of including the additional coefficients on the basis of the three variables.
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