Isogeometric simulation of thermal expansion for twin screw compressors

Abstract

Isogeometric Analysis (IGA) is a recently introduced computational approach intended to breach the gap between the Finite Element Analysis and the Computer Aided Design worlds. In this work, we apply it to numerically simulate thermal expansion of oil free twin screw compressors in operation. High global smoothness of IGA leads to a more accurate representation of the compressor geometry. We utilize standard tri-variate B-splines to parametrize the rotors, while the casing is modeled exactly by using NURBS. We employ the Galerkin version of IGA to solve the thermal expansion problem in the stationary case. The results allow to estimate the contraction of the clearance space between the casing and the rotors. The implementation is based on the open source C++ library G+Smo. This work is supported by the European Union within the Project MOTOR: Multi-ObjecTive design Optimization of fluid eneRgy machines.

An Overview of Geometry Plus Simulation Modules

“…From the simulation side, isogeometric simulation algorithms with the Galerkin approach, notably over nonconforming multi-patch physical domains are implemented and in a stable state. A module treating a large class of linear and non-linear elasticity problems was also released recently [7]. A module dedicated to isogeometric multigrid solvers on multipatch domains is also available [8].…”

Isogeometric parametrization inspired by large elastic deformation

“…The primary simplification γ can be re-expressed in terms of the original basis {B i (ξ ξ ξ)} P in two ways: either by applying h-and p-refinement − also known as knot insertion and degree elevation − or by projecting γ onto {B i (ξ ξ ξ)} i∈P in a manner analogous to (24)(25). The latter slightly changes the shape of γ which is insignificant since we have freedom in choosing the initial domain Ω 0 .…”

“…As the first example, we study the profile of a screw compressor's male rotor [24]. Its boundary is given as four cubic B-spline curves, and the domain is fairly simple so all considered parametrization techniques can be expected to perform well.…”