Shape Parameterization and Optimization of a Two-Stroke Engine

Abstract

We demonstrate a procedure for designing and optimizing the scavenging properties of a two-stroke engine. A method of surface design, known as the partial differential equation method, is used to represent the internal geometry of the engine. We then run steady-state computational uid dynamicscalculations to assess the scavenging ow inside the engine. To quantify the scavenging, the trapping ef ciency is used, and calculated values of this measure are obtained for different geometrical designs. We use a locally weighted regression-smoothing model to t the data, and then we optimize the resulting response surface. The optimization captured two local minima, one of which corresponds to accepted manufacturing practice and the other one is a new and counter-intuitive way of scavenging the engine, having optimum scavenging characteristics. Nomenclature C= contour M = mass of air n = number of particles r 0 = bore of the cylinder u, v = surface parametric coordinates V = volume of air X = vector of Cartesian coordinates of surface points X n = normal derivative along the boundary x, y, z = Cartesian coordinates xsu = derivative parameter of the transfer port, in x direction, on C 0 ysl = derivative parameter of the transfer port, in y direction, on C 1 ysu = derivative parameter of the transfer port, in y direction, on C 0 zsu = derivative parameter of the transfer port, in z direction, on C 0 a = smoothing parameter q = density Subscripts s = supplied t = trapped 0, 1 = upper and lower surface boundaries, respectively

Fast Surface Modelling Using a 6th Order PDE

“…The surface creation approach based on the solutions of PDEs was initially proposed by Bloor and Wilson, where a fourth order PDE with one shape control parameter was used [BW90]. Then, this fourth order PDE based approach was applied to a number of engineering design problems [BW97], [SBW00], [MBW01] and some applications in geometric modelling and computer graphics [BW00], [UBW99]. By superimposing a fourth order PDE and the motion equation in dynamics, Du and Qin investigated the issues of direct manipulation [DQ00], and solid modelling where the PDEs were solved with numerical methods [DQ01].…”

Deformation of Dynamic Surfaces

“…Partial differential equation (PDE) based modeling was firstly proposed by Bloor and Wilson [14] and applied in surface generation [15], surface blending [16], shape parameterization of a two-stroke engine [17] and fluid membranes and vesicles [18], and aerodynamic design of a flying wing [19] etc. In recent years, this modeling method has become more and more active.…”

Manipulation of Elastically Deformable Surfaces through Maya Plug-in

“…For instance, Sevant et al used partial differential equation method to parameterize a flying wing and obtained its design with maximized lift [19]. Mimis et al introduced PDE based surface modeling into design of a two-stroke engine and optimized its scavenging properties based on computational fluid dynamics calculations [20].…”