Analysis of dynamics of liquid jet injected into gaseous crossflow using proper orthogonal decomposition

Abstract

In this paper we present the results from the proper orthogonal decomposition (POD) on the liquid volume fraction scalar field from the detailed numerical simulations of turbulent liquid jet injection ($q = 6.6$, Re = \num{14000}, We = \num{2178}) into subsonic crossflowing air (Re = \num{570000}, We = \num{330}) to study the waves formed on the windward side of the liquid jet. The liquid/gas interface is captured using a coupled level set volume of fluid (CLSVOF) method. The method of snapshots technique is used in the POD to extract the proper orthogonal modes. A binarized form of the liquid volume fraction is given as input to POD. The modal energies and the least square truncation errors are presented for all the modes considered in this study. A travelling wave pattern is observed in the modes 5 and 6 on the windward side of the liquid jet. The waves in mode 5 are found to be \SI{90}{\degree} out-of-phase with those in mode 6. The approximate wavelength of these waves is in the order of the liquid jet diameter. The orthogonal modes are then used to compute the power spectral density (PSD) and the cross power spectral density (CPSD) to extract spectral information of the system dynamics. The characteristic frequency of mode pairs 5 and 6 is found to be \SI{15.8}{\kilo\hertz}. The out-of-phase observation is validated by the approximate match of the frequency at which \SI{90}{\degree} phase angle difference occurs and the characteristic frequency.