Investigation of Tip Clearance Phenomena in an Axial Compressor Cascade Using Euler and Navier-Stokes Procedures

Abstract

Three-dimensional Euler and Full Navier-Stokes computational procedures have been utilized to simulate the flow field in an axial compressor cascade with tip clearance. An embedded H-grid topology was utilized to resolve the flow physics in the tip gap region. The numerical procedure employed is a finite difference Runge-Kutta scheme. Available measurements of blade static pressure distributions along the blade span, dynamic pressure and flow angle in the cascade outlet region, and spanwise distributions of blade normal force coefficient and circumferentially averaged flow angle are used for comparison. Several parameters which were varied in the experimental investigations were also varied in the computational studies. Specifically, measurements were taken and computations were performed on the configuration with and without: tip clearance, the presence of an endwall, inlet endwall total pressure profiles and simulated relative casing rotation. Additionally, both Euler and Navier-Stokes computations were performed to investigate the relative performance of these approaches in reconciling the physical phenomena considered. Results indicate that the Navier-Stokes procedure, which utilizes a low Reynolds number k-ε model, captures a variety of important physical phenomena associated with tip clearance flows with good accuracy. These include tip vortex strength and trajectory, blade loading near the tip, the interaction of the tip clearance flow with passage secondary flow and the effects of relative endwall motion. The Euler computation provides good but somewhat diminished accuracy in resolution of some of these clearance phenomena. It is concluded that the level of modelling embodied in the present approach is sufficient to extract much of the tip region flow field information useful to designers of turbomachinery.

Numerical Simulation of Tip Clearance Effects in Turbomachinery

“…The abrupt transition from the blade passage to the tip gap, with the sharp corners at the blade tip and the large gradients in flow properties, make the use of typical H-or C-grids impractical. A commonly used approach, sometimes called the "thin blade approximation" or "pinched tip approximation," is to cusp the blade tip, e.g., Pouagare and Delaney (1986), Bansod and Rhie (1990), Kunz et al (1993), Storer and Barton (1991). This approach is reasonable for thin blade tips (e.g., compressors and pumps) and is only suitable for modeling the gross effects of the tip clearance flows as the tip geometry is not modeled correctly.…”

Computation of tip-leakage flow in a linear compressor cascade with a second-moment turbulence closure

“…These are associated with the presumed alignment of the principal axes of the rate-of-strain tensor and the Reynolds-stress tensor (pertinent primarily to linear EVMs), excessive diffusivity introduced in the eddy viscosity concept in general, the inability of most eddy-viscosity models to account for the stress anisotropy -which plays important role in all complex wall-bounded flows -as well as the difficulties in calibration of the empirical coefficients introduced in the non-linear models. While the failure of the standard linear eddy viscosity models to capture the complex three-dimensional phenomena is understandable, contrary to expectations the application of Non-Linear Eddy Viscosity and Algebraic Stress Models (NLEVM and ASM) -despite some noted improvementsresulted in mixed success in predicting various phenomena in turbomachinery in general (Kang and Hirsch, 1991;Cleack and Gregory-Smith, 1992;Suryavamshi and Lakshminarayana, 1992a,b;Kunz and Lakshminarayana, 1992;Borello and Rispoli, 2003;Gbadebo et al, 2004Gbadebo et al, , 2006 and, particularly, in the tip-leakage region (Crook et al, 1993;Kunz et al, 1993;Kang and Hirsch, 1993a,b;Corsini and Rispoli, 2005;Gdadebo et al, 2006). Admittedly, several papers claim satisfying results in predicting compressor cascade flows with EVMs in both 2D (Chen et al, 1998;Borello et al, 2003a,b;Chen and Leschziner, 1999) and 3D (Borello and Rispoli, 2003;Corsini and Rispoli, 2005).…”