A Simple Graphical Method for Constructing Two-Dimensional Supersonic Flows by Means of a Drafting Machine

1958 ◽  
Vol 25 (1) ◽  
pp. 69-70
Author(s):  
F. Edward Ehlers
Keyword(s):  
Graphical Method ◽  
Supersonic Flows ◽  
Two Dimensional

A RAPID GRAPHICAL SOLUTION FOR THE AEROMAGNETIC ANOMALY OF THE TWO‐DIMENSIONAL TABULAR BODY

Geophysics ◽  
1966 ◽  
Vol 31 (5) ◽  
pp. 963-970 ◽  
Author(s):  
R. J. Bean
Keyword(s):  
Inclination Angle ◽  
Geomagnetic Field ◽  
Graphical Method ◽  
The Body ◽  
Two Dimensional ◽  
Half Maximum ◽  
Graphical Solution ◽  
Magnetization Direction ◽  
Maximum Slope ◽  
Magnetic Latitude

A graphical method of determining the depth and other parameters of two‐dimensional tabular bodies by analysis of aeromagnetic anomalies is outlined. The method uses the inflection and half maximum slope points of anomalies having either two flanks or a single high gradient. Ratios of distances between these points are used to obtain a solution. The problem is simplified by combining angles of dip, magnetization direction and the inclination of the geomagnetic field in the plane of the profile into an apparent inclination angle. By use of the graphs, the depth, width, and apparent inclination angle can be determined rapidly from only a few simple measurements, so the method is especially suited for rapid interpretation of large aeromagnetic surveys by use of the observed profiles. Graphs are also given for locating the center or edge of the block, and the product of the intensity of magnetization and the dip of the body can be obtained by utilizing the maximum slope of the anomaly. By use of alternate values of the apparent inclination angle, the method can be used for any direction of magnetization at any magnetic latitude.

Two-Dimensional Rigid-Body Collisions With Friction

1992 ◽  
Vol 59 (3) ◽  
pp. 635-642 ◽  
Author(s):  
Yu Wang ◽  
Matthew T. Mason
Keyword(s):  
Rigid Body ◽  
Graphical Method ◽  
Correct Identification ◽  
Two Dimensional ◽  
Contact Mode ◽  
New Class ◽  
Tangential Impact ◽  
Approach Velocity ◽  
Conservation Principles ◽  
Analytical Expressions

This paper presents an analysis of a two-dimensional rigid-body collision with dry friction. We use Routh’s graphical method to describe an impact process and to determine the frictional impulse. We classify the possible modes of impact, and derive analytical expressions for impulse, using both Poisson’s and Newton’s models of restitution. We also address a new class of impacts, tangential impact, with zero initial approach velocity. Some methods for rigid-body impact violate energy conservation principles, yielding solutions that increase system energy during an impact. To avoid such anomalies, we show that Poisson’s hypothesis should be used, rather than Newton’s law of restitution. In addition, correct identification of the contact mode of impact is essential.

scholarly journals A CFD-Compatible Amplification Factor Transport Equation for Oblique Tollmien-Schlichting Waves in Supersonic Boundary Layers

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
JiaKuan Xu ◽  
Lei Qiao ◽  
Junqiang Bai
Keyword(s):  
Transport Equation ◽  
Amplification Factor ◽  
Flow Instability ◽  
Supersonic Flows ◽  
Boundary Layer Transition ◽  
Linear Stability Theory ◽  
Two Dimensional ◽  
Layer Transition ◽  
Low Speed ◽  
Tollmien Schlichting

Boundary layer transition is a hot research topic in fluid mechanics and aerospace engineering. In low-speed flows, two-dimensional Tollmien-Schlichting (T-S) waves always dominate the flow instability, which has been modeled by Coder and Maughmer from 2013. However, in supersonic flows, three-dimensional oblique Tollmien-Schlichting waves become dominant in flow instability. Inspired by Coder and Maughmer’s NTS amplification factor transport equation for two-dimensional Tollmien-Schlichting waves in low-speed flows and Kroo and Sturdza’s linear stability theory (LST) analysis results for oblique Tollmien-Schlichting waves in supersonic flows, a new amplification factor transport equation for oblique Tollmien-Schlichting waves has been developed based on LST. The compressible Falkner-Skan similarity equations are introduced to build the relationships between nonlocal variables and local variables so that all the variables used in the present model can be calculated using local variables. Applications of this new transport equation to the flows over supersonic flat plate, 3% thick biconvex airfoil, and one modified supersonic laminar airfoil show promising results compared with the standard LST analysis results.

Shock-bubble interactions: Generation and evolution of vorticity in two-dimensional supersonic flows

1988 ◽  
Vol 3 (1-4) ◽  
pp. 392-394 ◽  
Author(s):  
J W Chalmers ◽  
S W Hodson ◽  
K-H A Winkler ◽  
P R Woodward ◽  
N J Zabusky
Keyword(s):  
Supersonic Flows ◽  
Two Dimensional ◽  
Bubble Interactions

Calculating base pressures in two-dimensional supersonic flows

1966 ◽  
Vol 1 (3) ◽  
pp. 72-75 ◽  
Author(s):  
L. V. Gogish ◽  
G. Yu. Stepanov
Keyword(s):  
Supersonic Flows ◽  
Two Dimensional
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