Abstract
In this work, we develop a numerical strategy for analyzing the flows of an incompressible fluid in the gap between an arbitrarily shaped inner boundary that rotates inside a circular outer boundary. Such flows occur very commonly in turbomachinery applications. The numerical strategy is based on a noninertial frame of reference that is fixed to the rotating inner boundary so that Coriolis and angular acceleration effects have to be accounted for in its development. Since this strategy is based on a fixed mesh, it is much more economical and accurate than a general arbitrary Eulerian–Lagrangian strategy, which would typically require remeshing. In addition, we also conduct a numerical study for circular Couette flow with varying angular speed of the inner cylinder in an inertial frame of reference; such a study may prove useful in validating a theoretical stability analysis which currently seems to have been carried out only for the case of constant angular speed.
Highlights
This work develops a velocity-pressure integrated finite element formulation in a non-inertial frame for the general case of three-dimensional incompressible fluid flow without any simplifying assumptions such as potential flow
Kim and Decker [2] compared solutions obtained by the continuous-pressure formulation and penalty formulation, and concluded that both have comparable accuracy
We have developed a finite element strategy for analyzing flows in a noninertial frame of reference which can be used to solve for the fluid flow induced by rotating components inside a circular outer boundary, as is the case in most turbomachinery applications
Summary
This work develops a velocity-pressure integrated finite element formulation in a non-inertial frame for the general case of three-dimensional incompressible fluid flow without any simplifying assumptions such as potential flow. We attempt to solve the three-dimensional Navier–Stokes equations (without any simplifying assumptions such as potential flow) in a blade-fixed frame of reference In this approach, non-inertial body forces such as centrifugal and Coriolis forces have to be incorporated into the formulation. Since the outer boundary is circular in most turbomachinery applications, this approach is applicable to a large class of problems This strategy offers a computationally efficient method to solve fluid flows with an arbitrarily shaped inner rotating boundary. We conduct a numerical study of circular Couette flow for varying angular speeds of rotation of the inner cylinder with the outer cylinder fixed; such a study is of interest in its own right, but could prove useful in validating a theoretical stability analysis (which typically involves many simplifying assumptions)
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