Abstract



The unsteady laminar flow between two large rotating disks when one of them is impulsively started is described using the von Kármán similarity analysis to reduce the solution of the NavierStokes equations to a set of ordinary differential equations. It is found that the transient phenomenon consists of three distinct phases. Firstly, the development of the Ekman boundary layer, where a quasisteady Stewartsontype of flow is created. Secondly, angular momentum is initially diffused in the axial direction until the inward radial convection of angular momentum becomes dominating. Thirdly, a Batchelor flow is created once the Bödewadt boundary layer is developed and the entrainment of disk and stator boundary layers are balanced. The dependences of the characteristic dimensionless times on the Reynolds number based on the cavity gap for the second and third stages have been identified numerically and analytically. It is found that the diffusive part of the transient is bypassed if the flow, initially at rest, is perturbed with a small circumferential velocity. The flow and heat transfer transient during a ramp of finite duration has been computed numerically. The integral angular momentum and energy balances of the cavity have been performed in order to understand the energy and momentum budget of the cavity. It is concluded that the spinup and the spindown process of a rotor?stator cavity using a quasistationary approximation of the fluid, where the time derivatives are neglected, is questionable for realistic gas turbine applications. Finally, the selfsimilar solution is compared against twodimensional axisymmetric, steady and unsteady, laminar simulations to assess the limitations and validity of the selfsimilar analysis. It has been identified that in a closed squared cavity the outer shroud modifies the physics of the transient, but the general conclusions drawn from the onedimensional model are still valid.  
International

Si 
JCR

Si 
Title

Journal of Fluid Mechanics 
ISBN

00221120 
Impact factor JCR

2,893 
Impact info

Datos JCR del año 2017 
Volume

857 

10.1017/jfm.2018.755 
Journal number


From page

508 
To page

538 
Month

OCTUBRE 
Ranking
