Stability Analysis of the Flow over a Swept Forward-Facing Step using PIV Base Flows in a Nonorthogonal Coordinate System

2021 ◽  
Author(s):  
Koen J. Groot ◽  
Jenna L. Eppink
2021 ◽  
Vol 925 ◽  
Author(s):  
Wei He ◽  
Sebastian Timme

This article uses triglobal stability analysis to address the question of shock-buffet unsteadiness, and associated modal dominance, on infinite wings at high Reynolds number, expanding upon recent biglobal work, aspiring to elucidate the flow phenomenon's origin and characteristics. Infinite wings are modelled by extruding an aerofoil to finite aspect ratios and imposing a periodic boundary condition without assumptions on spanwise homogeneity. Two distinct steady base flows, spanwise uniform and non-uniform, are analysed herein on straight and swept wings. Stability analysis of straight-wing uniform flow identifies both the oscillatory aerofoil mode, linked to the chordwise shock motion synchronised with a pulsation of its downstream shear layer, and several monotone (non-oscillatory), spatially periodic shock-distortion modes. Those monotone modes become outboard travelling on the swept wing with their respective frequencies and phase speeds correlated with the sweep angle. In the limiting case of very small wavenumbers approaching zero, the effect of sweep creates branches of outboard and inboard travelling modes. Overall, triglobal results for such quasi-three-dimensional base flows agree with previous biglobal studies. On the contrary, cellular patterns form in proper three-dimensional base flow on straight wings, and we present the first triglobal study of such an equilibrium solution to the governing equations. Spanwise-irregular modes are found to be sensitive to the chosen aspect ratio. Nonlinear time-marching simulations reveal the flow evolution and distinct events to confirm the insights gained through dominant modes from routine triglobal stability analysis.


Author(s):  
Koen J. Groot ◽  
Qingqing Ye ◽  
Yue Zhang ◽  
Fabio Pinna ◽  
Bas van Oudheusden

Author(s):  
Xiaowei Tang ◽  
Zerun Zhu ◽  
Rong Yan ◽  
Chen Chen ◽  
Fangyu Peng ◽  
...  

The traditional stability analysis by only considering cutting depth-spindle speed lobe diagram is appropriate for parameters optimization and efficiency improvement of the five-axis ball-end milling. However due to the complicated cutter-workpiece engagement (CWE) of bull-nose end cutter in five-axis milling, the maximal cutting depth may not produce the maximal material removal rate (MRR). Thus, the traditional stability analysis is not suitable for the five-axis bull-nose end milling in parameters optimization, and this paper presents a new stability analysis method to analyze the effect of tool orientation on machining efficiency for five-axis bull-nose end milling. In the establishing of stability prediction model, coordinate transformation and vector projection method are adopted to identify the CWE and dynamic cutting thickness, and the geometrical relationship of frequency response function (FRF) coordinate system and cutting force coordinate system with variable tool orientation is derived to establish the conversion of FRF and cutting force in stability equation. Based on the CWE sweeping, the cutting area along the feed direction is calculated to realize the critical MRR analysis in the stability model. Based on the established stability prediction model, the effects of tool orientation on critical cutting depth and MRR considering the chatter constraint are analyzed and validated by the cutting experiments, respectively. The lead-tilt diagram, which not only gives the boundary of stability region but also describes the contour line for MRR, is proposed for the further tool orientation optimization.


1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.


1975 ◽  
Vol 26 ◽  
pp. 21-26

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.


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