CFD Analysis of Premixed Combustion in a Two Stroke Polygon Engine

The numerical modeling of the premixed combustion occurring in the chamber of a polygon engine is presented in this paper. This research is being carried out to support the analysis and design of a lightweight, two-stroke, six-sided, in-plane, polygon engine. Results for average combustion chamber temperature, turbulent flame speed, progress variable, and Damkohler number versus piston position are presented for methane (CH4), diesel (C10H22), and ethanol (C2H50H) fuels, respectively.

Design and Analysis of a Lightweight Polygon Engine

Current trends in engine design have pushed the state-of-the-art regarding high power-to-weight ratio gasoline engines. Newly developed engine systems have a power to weight ratio near 1 hp per pound. The engine configuration presented herein makes it possible to package a large number of power producing pistons in a small volume resulting in a power to weight ratio near 2 hp per pound, which have never before been realized in a production engine. The analysis and design of a lightweight, two-stroke, 6 side, in-plane, polygon engine having a geometric compression ratio of 15.0, actual compression ratio of 8.8 and piston speed of 3500 ft/min are presented in this investigation. Power output, kinematic modeling, and weight estimates are presented.

SINGULARITIES OF STATIONARY SOLUTIONS TO THE VLASOV–POISSON SYSTEM IN A POLYGON

We present an existence result for the stationary Vlasov–Poisson system in a bounded domain of ℝN, with more general hypotheses than considered so far in the literature. In particular, we prove the equivalence of the kinetic approach (which consists in looking for the equilibrium distribution function) and the potential approach (where the unknown is the electrostatic potential at equilibrium). We study the dependence of the solution on parameters such as the total mass of the distribution, or those entering in the boundary conditions of the potential. Focusing on the case of a plane polygon, we study the singular behavior of the solution near the re-entrant corners, and examine the dependence of the singularity coefficients on the parameters of the problem. Numerical experiments illustrate and confirm the analysis.

EXISTENCE AND REGULARITY RESULTS FOR THE STOKES SYSTEM WITH NON-SMOOTH BOUNDARY DATA IN A POLYGON

We discuss the problem of existence and uniqueness of solutions for the nonhomogeneous Stokes system in a plane polygon with non-smooth boundary data.

Generating Swept Volumes With Instantaneous Screw Axes

The instantaneous screw axis is used in the generation of the swept volume of a moving object. The envelope theory is used to determine the boundary surfaces of the swept volume. Specifically, the envelope surfaces generated by a plane polygon, cylindrical and spherical surfaces are presented. Furthermore, the ruled surfaces generated by edges of the moving object are discussed.

APPROXIMATING POLYGONS AND SUBDIVISIONS WITH MINIMUM-LINK PATHS

We study several variations on one basic approach to the task of simplifying a plane polygon or subdivision: Fatten the given object and construct an approximation inside the fattened region. We investigate fattening by convolving the segments or vertices with disks and attempt to approximate objects with the minimum number of line segments, or with near the minimum, by using efficient greedy algorithms. We give some variants that have linear or O(n log n) algorithms approximating polygonal chains of n segments. We also show that approximating subdivisions and approximating with chains with. no self-intersections are NP-hard.

Explicit formulae for polygonally generated shape-densities in the basic tile

Kendall and Le [4] gave an exact algorithm for the computation of a polygonally generated (auxiliary) shape-density m̃(x, y) which we used to obtain ‘exact’ numerical densities for given (x, y). Here I derive an explicit formula for m̃(x, y), for an arbitrary convex plane polygon K, valid when the shape-point (x, y) lies in what will be called the ‘(upper) basic tile’ of the associated singular tessellation. In most circumstances this is all that is needed for the statistical analysis of collinearities.