Proper orthogonal decomposition analysis for two-oscillating grid turbulence with viscoelastic fluids

Abstract

In this article, the experiments of two-oscillating grid turbulence with viscoelastic fluids were carried out using particle image velocimetry. Two classical drag-reducing additives with viscoelastic characteristics were chosen: polymer (polyacrylamide) and cationic surfactant (cetyltrimethyl ammonium chloride). In order to investigate the viscoelastic effect on coherent structures, proper orthogonal decomposition was performed to identify coherent structures based on particle image velocimetry data. The results show that the minimum number for eigenmodes required for capturing coherent structures, which contains 90% of total turbulent kinetic energy, is 127, 19, and 117 for the Newtonian fluid case, 25 ppm polyacrylamide solution case, and 25 ppm cetyltrimethyl ammonium chloride solution case at grid oscillating frequency f = 7.5 Hz, respectively. It means that coherent structures can be inhibited due to the addition of polyacrylamide additives but not remarkable in 25 ppm cetyltrimethyl ammonium chloride solution case, in other words, the decrease in flow complexity in 25 ppm polyacrylamide solution case. This phenomenon also appears at grid oscillating frequency f = 5 Hz. However, as cetyltrimethyl ammonium chloride solution concentration increases up to 50 ppm, the cetyltrimethyl ammonium chloride solution case shows similar trends as those in 50 ppm polyacrylamide solution case (the number for eigenmodes required for capturing coherent structures is approximate). Therefore, compared with a channel flow with cetyltrimethyl ammonium chloride solution, there exists the larger critical concentration in two-oscillating grid turbulence to show turbulence suppression effect.