Some Three-Dimensional Effects of Rotating Stall
SUMMARY A small perturbation analysis of rotating stall in inviscid, incompressible flow is developed from an analysis of Yeh. An isolated blade row is considered having a blade height which is not small compared to the msan radius. A criterion is derived for tie occurrence of rotating stall, the speed of stall propagation and the possible number of stall cells involved. From this the frequency of circumferential flow disturbances can be obtained. An example is given of an application Of the analysis. The main assumptions made are that a large number of small amplitude stall cells are induced at onset of stall, that the radial shift of the streamlines is small and that the absolute exit flow angle is small. Possible explanations are suggested for the observed changes in number of stall cells.
Vortex Structure and Kinematics of Encased Axial Turbomachines
This paper models the kinematics of the vortex system of an encased axial turbomachine at part load and overload applying analytical methods. Thus far, the influence of the casing and the tip clearance on the kinematics have been solved separately. The vortex system is composed of a hub, bound and tip vortices. For the nominal operating point φ ≈ φ opt and negligible induction, the tip vortices transform into a screw. For part load operation φ → 0 the tip vortices wind up to a vortex ring, i.e., the pitch of the screw vanishes. The vortex ring itself is generated by bound vortices rotating at the angular frequency Ω . The hub vortex induces a velocity on the vortex ring causing a rotation at the sub-synchronous frequency Ω ind = 0.5 Ω . Besides, the vortex ring itself induces an axial velocity. Superimposed with the axial main flow this results in a stagnation point at the tube wall. This stagnation point may wrongly be interpreted as dynamic induced wall stall. For overload operation φ → ∞ the vortex system of the turbomachine forms a horseshoe, i.e., the pitch of the screw becomes infinite. Both hub and tip vortices are semi-infinite, straight vortex filaments. The tip vortices rotate against the rotating direction of the turbomachine due to the induction of the hub vortex yielding the induced frequency Ω ind = − 0.5 Ω / s with the tip clearance s.
Thermal incompatibility analysis of metal-ceramic systems based on flexural displacement data.
The feasibility of simple tests or analytical methods for prediction of residual stress states in metal-ceramic (MC) prostheses has not been demonstrated. Biomaterial metal-ceramic strips have been proposed to provide sensitive measures of transient and residual stress states through the measurement of midpoint deflection after cooling from the ceramic sintering temperature. The objective of this study was to apply the elastic-viscoelastic analogy to calculate transient and residual midpoint deflections in MC biomaterial strips and to compare these values with deflections measured with a beam-bending viscometer (BBV). Calculations and measurements were made for five MC systems that were found from a clinical study to be "thermally compatible" systems. Metal strips, 64 mm in length, 3 mm wide, and either 0.5 mm, 1.0 mm, or 2.0 mm in thickness, were veneered with four 0.25-mm thick layers of opaque porcelain. Midpoint deflection of the MC strips (ceramic oriented in the posterior position) was measured during cooling from an initial temperature of 700 degrees C. In general, the directions of the measured residual deflections did not agree with the "textbook" convention that negative deflections are associated with positive thermal contraction mismatch (alpha(M) - alpha(c) > 0) regardless of metal thickness. For a metal thickness of 0.5 mm, the residual midpoint deflection for all thermal contraction mismatch cases, except one, was positive (upward deflection) whereas the residual midpoint deflections were all negative when the metal thickness was increased to 1 or 2 mm, independent of the thermal contraction mismatch. The best agreement between calculated and measured values of residual midpoint deflection (+16 microns vs. +14 +/- 2.3 microns, respectively was obtained for MC biomaterial strips with a Ni-Cr alloy (0.5 mm thick) while the largest difference (+346 microns vs. +61 +/- 43.8 microns) was obtained for MC bimaterial strips with a Au-Pd allow (0.5 mm thick). In all but one case, changes in deflection direction as a function of metal thickness were correctly predicted by the viscoelastic analysis. The results of this study indicate that a viscoelastic model is useful for estimating thermal compatibility conditions of MC systems.