One-dimensional calculation approach for gaseous clearance flows

Abstract

Clearance flows do strongly influence the efficiency of dry-running positive displacement machines. To model the operation behaviour of the machines an accurate prediction of the clearance mass flows is crucial. If a chamber model simulation is used, the clearance mass flows are commonly estimate with simple equation to keep the computational effort low. Therefore, regression functions or coefficient databases are built into simulation. However, finding such functions or coefficients is a challenging and expensive task since many boundary conditions and geometry parameters must be varied in experiment or simulation. To reduce the effort of clearance analysis this paper presents a one-dimensional approach to estimate the clearance mass flow in e.g. dry-running screw-type compressors, based on the well-known differential equation of A.H. Shapiro for compressible flow of ideal gases. The friction is modelled with respect to laminar and turbulent flow. The flow separation and the friction of laminar flow are modelled based on the solutions of the Jeffery-Hamel flow. The friction in the turbulent regime is modelled by the Blasius expression, while the flow separation criteria is assumed to be the same as for laminar flow. The moving clearance wall is modelled assuming a superposition of Couette and Poiseuille flow. In addition, the heat transfer between gas and clearance boundary as well as gas rarefaction can also be optionally modelled. Results of the one-dimensional approach are compared to measurements and 3D-CFD simulations from the literature, varying Reynolds number and wall velocity.