The Transient Motion of a Ramp-Core Supersonic Dislocation

2000 ◽  
Vol 68 (4) ◽  
pp. 656-659 ◽  
Author(s):  
X. Markenscoff ◽  
L. Ni
Keyword(s):  
Tangent Point ◽  
Supersonic Speed ◽  
Transient Motion ◽  
Delta Sequence ◽  
Core Dislocation

The transient motion of a ramp-core dislocation spreading from −∞<x<∞ and jumping from rest to a supersonic speed in the x direction, is investigated by analysis on the complex transform plane. The new result of this analysis is that, instead of the Mach cone of the Volterra dislocation, there are two lines of discontinuity (of the stress) propagating in the ±z directions, inside of which there are arctan delta sequence (ε≠0) radiated supersonic fields, as well as subsonic fields. The lines of discontinuity arise at the tangent point of the Mach wavefront (ε=0) to the cylinder with radius r=c2t.

Edges of Regression and Limit Normal Point of Conjugate Surfaces1

1998 ◽  
Vol 122 (4) ◽  
pp. 419-425 ◽  
Author(s):  
Ningxin Chen
Keyword(s):  
Differential Geometry ◽  
Contact Boundary ◽  
Boundary Line ◽  
Tangent Point ◽  
Common Tangent ◽  
Numerical Examples ◽  
Envelope Surface ◽  
The Common ◽  
Conjugate Surfaces ◽  
Definition Of

The presented paper utilizes the basic theory of the envelope surface in differential geometry to investigate the undercutting line, the contact boundary line and the limit normal point of conjugate surfaces in gearing. It is proved that (1) the edges of regression of the envelope surfaces are the undercutting line and the contact boundary line in theory of gearing respectively, and (2) the limit normal point is the common tangent point of the two edges of regression of the conjugate surfaces. New equations for the undercutting line, the contact boundary line and the limit normal point of the conjugate surfaces are developed based on the definition of the edges of regression. Numerical examples are taken for illustration of the above-mentioned concepts and equations. [S1050-0472(00)00104-5]

Surface pressures on a wing moving with supersonic speed

1974 ◽  
Vol 341 (1625) ◽  
pp. 177-193 ◽  
Keyword(s):  
Supersonic Flow ◽  
Delta Wing ◽  
Leading Edge ◽  
Ideal Gas ◽  
Numerical Results ◽  
Coordinate Surface ◽  
Supersonic Speed ◽  
Extrapolation Procedure ◽  
Specific Heats ◽  
Limiting Values

Estimates for pressures on the surface of a given delta wing at zero incidence in a steady uniform stream of air are obtained by numerically integrating two semi-characteristic forms of equations which govern the inviscid supersonic flow of an ideal gas with constant specific heats. In one form of the equations coordinate surfaces are fixed in space so that the surface of the wing, which has round sonic leading edges, is a coordinate surface. In the other, two families of coordinates are chosen to be stream-surfaces. For each form of the equations, a finite difference method has been used to compute the supersonic flow around the wing. Convergence of the numerical results, as the mesh is refined, is slow near the leading edge of the wing and an extrapolation procedure is used to predict limiting values for the pressures on the surface of the wing at two stations where theoretical and experimental results have been given earlier by another worker. At one station differences between the results given here and the results given earlier are significant. The two methods used here produce consistent values for the pressures on the surface of the wing and, on the basis of this numerical evidence together with other cited numerical results, it is concluded that the pressures given here are close to the true theoretical values.

Numerical Multiphysics Modeling of Microdroplet Motion Dynamics in Digital Microfluidic Systems

2010 ◽  
Author(s):  
Ali Ahmadi ◽  
Jonathan F. Holzman ◽  
Homayoun Najjaran ◽  
Mina Hoorfar
Keyword(s):  
Numerical Algorithm ◽  
Moving Boundary ◽  
Microfluidic Systems ◽  
Multiphysics Modeling ◽  
Transient Motion ◽  
Proposed Model ◽  
Digital Microfluidic ◽  
Motion Dynamics

In this paper a novel numerical algorithm is proposed for modeling the transient motion of microdroplets in digital microfluidic systems. The new methodology combines the effects of the electrostatic and hydrodynamic pressures to calculate the actuating and opposing forces and the moving boundary of the microdroplet. The proposed model successfully predicts transient motion of the microdroplet in digital microfluidic systems, which is crucial in the design, control and fabrication of such devices. The results of such an analysis are in agreement with the expected trend.

Aerodynamic optimisation of the rocket plane in subsonic and supersonic flight conditions

2017 ◽  
Vol 231 (12) ◽  
pp. 2266-2281 ◽  
Author(s):  
Marcin Figat ◽  
Agnieszka Kwiek
Keyword(s):  
Mach Number ◽  
Main Part ◽  
Numerical Study ◽  
Aerodynamic Characteristics ◽  
Aerodynamic Design ◽  
Supersonic Speed ◽  
Supersonic Flight ◽  
Special Vehicle ◽  
Speed Regime ◽  
The Impact

This paper presents the results of a numerical study of the aerodynamic shape of the Rocket Plane LEX. The Rocket Plane is a main part of the Modular Airplane System – MAS; a special vehicle devoted to suborbital tourist flights. The Rocket Plane was designed for subsonic and supersonic flight conditions. Therefore, the impact of the Mach number should be considered during the aerodynamic design of the Rocket Plane. The main goal of the investigation was to determine the sensitivity of the Rocket Plane aerodynamic characteristics to the Mach number during the optimisation of the LEX geometry. The paper includes results of the optimisation process for Mach number from the range Ma = 0.5 to Ma = 2.5. These results reveal that the aerodynamic characteristics of models optimised for the subsonic and transonic regime of Mach numbers (up to Ma = 1) were also improved for the supersonic speed regime. However, in the case of models optimised for the supersonic flight regime the aerodynamic characteristics in subsonic flight regime, are inferior compared to the model before the optimisation process.

Sign in / Sign up

Export Citation Format

Share Document