Converged statistics for time-resolved measurements in low-speed axial fans using high-frequency response probes

Abstract

Fast-response probes in multistage turbomachinery are typically used to measure unsteady flows and turbulence in a number of traverse locations throughout the machine (rotor-stator interregions, inlet and outlet sections, tip clearance gaps…). When used intensively, they provide complete information of time-resolved flow structures, including wake patterns, wake mixing, wake-wake and rotor-wake interactions or turbulence transport in 2D planes and even 3D pictures if the raw signals are post-processed accurately. The segregation between deterministic, unsteady features and turbulent scales is essential to understand the unsteady mechanisms responsible for the energy transfer and requires an accurate selection of the sampling frequencies and the total length of the measured traces to assure a valid statistical reduction. Similar considerations must be made if they are filtered in a frequency basis (for example, filtering low-scale turbulence or extracting only BPF components), employing welldesigned periodograms or power spectra with minimum scatter and large periods of time integration. This work presents the effect of number of periods (ensembles), resolution in which the averaged periods are reconstructed and turbulence intensity on the experimental accuracy of ensemble-averaged measurements in low-speed axial fans using fast-response probes. In particular, the statistical analysis is established in terms of convergence (residuals) between timeresolved traces retrieved using different sampling frequencies and number of total samples. The possible effects of three-dimensionality, the measured regions (hub, tip, midspan) or the sensibility to turbulence levels is also explored. A technique to quantify the convergence of the phase-locked averaging (PLA) processes is applied to a low-speed axial fan, with twin configurations of rotor-stator and stator-rotor arrangements. As a starting point, a concise survey of usual practices employed by other authors in the literature for axial fans and compressors is firstly reviewed, in order to identify fundamental parameters and values typically adopted to guarantee convergence. Finally, typical requirements are given as a function of the variable analyzed, the wake pattern to be described or the global disorder of the flow structures inside axial flow fans.

LES-based simulation of the time-resolved flow for rotor-stator interactions in axial fan stages

“…They are derived from maps of the time-averaged turbulence and illustrate the relationship between both variables. This direct correspondence between the required convergence threshold and local time-mean turbulence intensity has been previously demonstrated (see annex in Fernández Oro et al , 2014). Note the evident similarities between the post-processed and theoretical values.…”

“…This section concludes analyzing the number of ensemble averages needed in LES computations to obtain a fully converged time-resolved flow. All the basic guidelines have been previously discussed in Fernández Oro et al (2014) for the experimental measurements from this axial fan. In particular, a statistical indicator of convergence (i.e.…”

Experimental investigation on the effect of load distribution on the performances of a counter-rotating axial-flow fan

“…It would be very interesting to better characterize these interactions with phase-locked time-resolved measurements such as described in Refs. [12,13]. The effect of the number of blades in each rotor may also be addressed in forthcoming experiments, with JW1 rotors of same blade cascade parameters but different blade numbers, and focusing on acoustical behaviour of the counter-rotating stages.…”

“…Strong unsteady interactions between the rotors may lead to large acoustic noise emission [11] and may affect the performances of the stage [12,13]. When designing a counter-rotating stage, some parameters such as the distribution of the total work between the two rotors or the ratio of the rotation rates have to be chosen, this choice being most often somehow arbitrary.…”

Turbulence Transport in Rotor-Stator and Stator-Rotor Stages of Axial Flow Fans

“…All these assumptions, based on the extrusion of a two-dimension (2D) section of the fan with periodic conditions, have been already experimentally verified [10] for three different operating conditions: 100, 85 and 70% of the nominal flow rate. Furthermore, LES computations have been extended for a wide number of blade events, in order to obtain a representative statistical convergence of the averaged results [11].…”