Phase-averaged flow statistics in compressors using a rotated hot-wire technique

Abstract

produces a flow field that is inherently unsteady, threedimensional and multi-scale.It is customary to divide the unsteadiness in compressors into two categories: (1) deterministic fluctuations related to the shaft and blade frequencies and (2) broadband stochastic fluctuations related to naturally occurring turbulence. The mean square of (1) and (2) are manifest as deterministic stresses and Reynolds stresses, respectively. Furthermore, statistical moments may exhibit periodicities in both space and time. The space-time dependence of flow statistics significantly complicates the closure of the phase-averaged Navier-Stokes equations, relative to the traditional Reynolds-averaged formulation (Reynolds and Hussain 1972).The numerical prediction of compressor performance and stability rank amongst the greatest achievements of modern computational fluid dynamics (CFD) (Bradshaw 1996). Several frameworks for compressor CFD exist and include: (1) the steady-state mixing-plane method (Denton 1990; Dawes 1991; (2) the unsteady sliding-plane method (Rai 1989); and (3) the average-passage method (Adamczyk 1985). Depending on which method is adopted, the action of deterministic stresses, Reynolds stresses, or their combined effect should be modeled properly to achieve physically meaningful results. However, it is widely acknowledged that contemporary modeling practice can compromise the reliability of CFD results (Denton 2010). Ultimately, modeling uncertainties will only be reduced through improved physical understanding.To improve the understanding of momentum and energy exchange mechanisms in compressor annuli, it is imperative to acquire scale-resolved measurements in realistic, rotating, multi-bladed environments. Steady-state data are of limited value, since statistical moments of fluctuating quantities cannot be evaluated. Useful data must be highly Abstract A technique based on a rotated hot wire has been developed to characterise the unsteady, three-dimensional flow field between compressor blade rows. Data are acquired from a slanted hot wire rotated through a number of orientations at each measurement point. Phase-averaged velocity statistics are obtained by solving a set of sensor response equations using a weighted, non-linear regression algorithm. The accuracy and robustness of the method were verified a priori by conducting a series of tests using synthetic data. The method is demonstrated by acquiring a full set of phase-averaged flow statistics in the wake of a compressor stator blade row. The technique allows three components of phase-averaged velocity, six components of phase-averaged deterministic stress, and six components of phase-averaged Reynolds stress to be recovered using a single rotated hot-wire probe.