Experimental studies on the frequency selection in flat plate wakes: mean flow stability analyses and low dimensional modeling

TL;DR

This study combines experimental measurements, mean flow stability analysis, and low-dimensional POD modeling to accurately predict vortex shedding frequencies in flat plate wakes, revealing the importance of nonlinear interactions.

Contribution

It introduces a novel low-dimensional POD-based model for flat plate wakes that accurately estimates shedding frequency using only two modes.

Findings

Mean flow stability analysis matches experimental shedding frequencies.

A two-mode POD model accurately predicts vortex shedding frequency.

Nonlinear interactions between mean flow and harmonics are significant.

Abstract

We investigate the global frequency selection of two-dimensional vortex shedding in the flat plate wake. The analysis is based on the mean flow velocity profiles obtained from experimental measurements carried out for two values of Reynolds number, 1850 and 3350, which are based on the plate thickness and the free-stream velocity. Two different trailing edge geometries of the flat plate are considered in this study: blunt and circular. By performing local spatio-temporal analyses on the measured mean flow velocity profiles, we estimate the global shedding frequency of the flow. This is in excellent agreement with the shedding frequency measured experimentally. To complement the study, we carry out a low-dimensional modeling based on the proper orthogonal decomposition (POD) of the flow fields which is novel for flat plate wakes. We observe that a model based on only two POD modes produces an accurate estimate of the global shedding frequency. Our results also highlight the role of the nonlinear interaction strength between the mean flow with the higher harmonics thereby experimentally supporting the theoretical criterion outlined in Sipp & Lebedev (JFM 2007).