The Variable Cross-Section Helix Turning Trajectory Algorithm Used on the Middle-Convex and Varying Ellipse Piston Skirt

In order to turning the skirt of middle-convex and varying ellipse piston, this paper proposes a Variable Cross-section Helix Turning Trajectory (VCHTT) algorithm. it divide the turning trajectory of the piston skirt into transversal and helix, then obtain the coordinates of ellipse transversal cutter-contact points on the basis of centric polar radius arc interpolation (CPRAI) algorithm, and uses line surface intersection method to obtain the coordinates of helix cutter-contact points on the middle-convex and varying ellipse piston skirt. At last，merge two coordinates matrices to obtain the final coordinate surface of cutter-contact points of turning tool. With comparison, it finds that the VCHTT algorithm improves the interpolation accuracy by 0.04um than other methods.

The Atomic Geometry of the Reconstructed (001) Surface of the Rutile Phase of SnO2

The tight-binding total energy formalism developed for tetrahedrally coordinated compound semiconductors has been extended to rutile-structure oxides and applied to calculate the surface atomic geometry and electronic structure of SnO2 (001). Two stable structures, separated by an energy barrier, are found. The first consists of slightly relaxed surface geometry with the top layer oxygen atoms relaxed outward by approximately 0.12A, and cations inward by 0.25A. The second geometry is a more massively reconstructed surface in which the four-coordinate surface Sn atoms attain highly distorted tetrahedral coordination.

General Curved Surface Fitting and Calculation of Flow Along Arbitrarily Twisted Stream Surface

This paper consists of two parts. (1) General curved surface fitting and grid refining. A method of fitting a set of given discrete points on several stream lines to give a smooth and arbitraily twisted stream surface was developed. Based upon the small deformation theory for thin plate, the Kirchhoff’s Equation was solved and twofold transformations were incorporated. The first step is the transformation from physical surface into computational surface and the second is affine transformation. The accuracy of the result is about 0.004% and the CPU time needed is reasonable for engineering application. Then the refined computational grid and the calculation for the geometrical quantities of the grid are carried out on the fitted surface. (2) Calculation of the flow along the fitted stream surface. Employing non-orthogonal curvilinear coordinate system, the fitted stream surface is selected as a coordinate surface, so that there are only two velocity components even when the stream surface is arbitrarily twisted, and it is very convenient to define the stream function. The general equation for the quasi-linear stream function governing the flow along the fitted stream surface was employed. This was solved with the method of direct decomposition of matrix. The numerical examples are also included in this paper. The present method can be used for S1 and S2 stream surfaces and other engineering calculations.

Surface pressures on a wing moving with supersonic speed

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.

A coordinate system based on a twisting null geodesic congruence

A coordinate system based on a twisting null geodesic congruence is developed. The various freedoms of choice are investigated and a short theorem regarding the choice of one coordinate surface is proved.

Remarks on the problem of slow motions in a rotating fluid

This note is concerned with the problem of the slow motions of an inviscid, incompressible rotating fluid, and in particular with the motion of a sphere along the axis of rotation. This problem was studied recently by Stewartson (2), who overcomes the principal mathematical difficulty, viz. that of formulating the problem in a coordinate system in which the appropriate differential equation can be solved simply and in which the sphere is a coordinate surface, by a very elegant transformation of independent variables. Stewartson, however, uses inappropriate initial conditions. It is the purpose of this note to discuss the question of initial conditions in the light of results previously obtained by the writer (1).