On the transient behaviour of a laminar rotor-stator cavity

Corral Garcia, Roque and Romera Hijano, David (2018). On the transient behaviour of a laminar rotor-stator cavity. "Journal of Fluid Mechanics", v. 857 ; pp. 508-538. ISSN 0022-1120. https://doi.org/10.1017/jfm.2018.755.


Title: On the transient behaviour of a laminar rotor-stator cavity
  • Corral Garcia, Roque
  • Romera Hijano, David
Item Type: Article
Título de Revista/Publicación: Journal of Fluid Mechanics
Date: October 2018
ISSN: 0022-1120
Volume: 857
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Matemática Aplicada a la Ingeniería Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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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 Navier?Stokes 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 quasi-steady Stewartson-type 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 spin-up and the spin-down process of a rotor?stator cavity using a quasi-stationary approximation of the fluid, where the time derivatives are neglected, is questionable for realistic gas turbine applications. Finally, the self-similar solution is compared against two-dimensional axisymmetric, steady and unsteady, laminar simulations to assess the limitations and validity of the self-similar 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 one-dimensional model are still valid.

Funding Projects

Government of SpainDPI2017-84700-RUnspecifiedUnspecifiedFenómenos aeromecánicos en motores de aviación
Universidad Politécnica de MadridP1614120148UnspecifiedUnspecifiedUnspecified

More information

Item ID: 57607
DC Identifier: http://oa.upm.es/57607/
OAI Identifier: oai:oa.upm.es:57607
DOI: 10.1017/jfm.2018.755
Official URL: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/on-the-transient-behaviour-of-a-laminar-rotorstator-cavity/3F23278A5E4C211EF1DBBB6D5D806CC2
Deposited by: Memoria Investigacion
Deposited on: 18 Feb 2021 10:44
Last Modified: 18 Feb 2021 10:44
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