Numerical investigation of spray self-pulsation characteristics of liquid-centered swirl coaxial injector with different recess lengths

Abstract

The self-pulsation characteristics of a liquid-centered swirl coaxial (LCSC) injector are investigated numerically based on the coupled level set and volume of fluid (CLSVOF) model. Effects of recess length on self-pulsation characteristics are evaluated and discussed. The results demonstrate the crucial role of recess length in exciting self-pulsation. As the recess length increases, spray patterns vary from stable hollow cone to self-pulsated “Christmas tree” shape, and the characteristic frequency increases marginally. Compared with the stable spray, when self-pulsation occurs, the droplets are distributed more widely in the radial direction. Self-pulsation is easily excited under conditions with the critical mixing flow. Several methods to suppress self-pulsation have been proposed. The breakup of the liquid sheet is successively dominated by surface waves and spray self-pulsation as the recess length increases. The waves in both the azimuthal and the axial directions are captured and investigated. The unstable waves are composed of sinuous mode and varicose mode. The varicose waves are responsible for the primary breakup of liquid sheet. The results for the self-pulsated spray suggest that the primary breakup of the liquid sheet is coupled with pressure oscillation inside the confined region. Self-pulsation of recessed LCSC injector is suggested to be caused by the periodical blocking of the annular gap by the liquid sheet.

Introduction

Various applications, such as rocket, diesel, and gas turbine engines, are functioning with swirl coaxial injectors because of their efficient mixing and atomization performances (Im et al., 2015; Yang and Anderson, 1995). Typically, the gas-liquid swirl coaxial injectors can be divided into two categories, namely gas-centered swirl coaxial injector (GCSC) (Lightfoot et al., 2006; Villasmil et al., 2016) and liquid-centered swirl coaxial (LCSC) injector (Bazarov and Yang, 1998). The atomization process of an LCSC injector is shown in Fig. 1. The liquid is injected into the swirl chamber through tangential entries. As a result, a swirling liquid film is formed. Due to centrifugal force, an empty gas-core is generated around the centerline of the injector, and the liquid sheet will expend after ejecting from the inner injector. An annular gas stream is injected through the annular gap, as indicate in Fig. 1. Breakup of the liquid sheet depends highly on the gas-liquid interaction (Chu et al., 2020). Under certain operating conditions and injectors with certain geometrical parameters, the LCSC injector is known to experience spray self-pulsation (Bazarov and Lul'ka, 1978). Because spray self-pulsation may introduce harmful disturbance to the combustion chamber and induce combustion instability, this phenomenon must be controlled (Bai et al., 2020).

Self-pulsation is defined as the pressure and mass flow rate oscillations resulting from a time-delayed feedback between liquid and gas (Im et al., 2005). Significant efforts have been made to explore the mechanism of self-pulsation, in order to control it. Bazarov et al. (Bazarov, 1995; Bazarov and Lul'ka, 1978) conducted a pioneering theoretical and experimental investigation on self-pulsation. They found that self-pulsation arises from a time-delayed feedback caused by transient hydro-resistance between liquid and gas (Bazarov, 1995). Im et al. (Im et al., 2009, 2005) suggested that self-pulsation might result from the dominant wave of the liquid sheet. Hung et al. (Yuhui et al., 1998) developed a simplified acoustic model to compare the self-pulsation frequency and resonance frequency. They concluded that self-pulsation was caused by the resonance between the annular gas and the gas-core of the swirling liquid sheet. Applying a two-dimensional swirling symmetrical model, Bai et al. (Xiao et al., 2018) studied self-pulsation both experimentally and numerically. They attributed the self-pulsation mechanism of the recessed LCSC injector to the periodic blocking action of the liquid sheet. Nevertheless, violent self-pulsation was also discovered for non-recessed LCSC injectors by Eberhart and Frederick, (2017b). Besides, they concluded that self-pulsation was caused by the K-H instability (Eberhart and Frederick, 2017a). Recently, Chu et al. (Chu et al., 2020) performed a three-dimensional numerical investigation into the spray characteristics of a non-recessed LCSC injector and proposed that the vortex shedding of the spray induced self-pulsation. The mechanisms of recessed and non-recessed LCSC injectors seem different. Despite considerable efforts, the mechanism of self-pulsation is not yet fully understood.

During self-pulsation, the spray patterns oscillate periodically like a “Christmas tree” (Bai et al., 2019) or “string” (Im and Yoon, 2008). According to Kang et al. (Kang et al., 2014), the spray pattern is determined by the gas-core of the injector. Generally, self-pulsation is accompanied by painful screams (Yuhui et al., 1998). The acoustic frequency is almost the same as the spray oscillation frequency; therefore, the self-pulsation frequency can be characterized not only by the spray oscillation frequency but also by the acoustic frequency (Im et al., 2005). Im et al. (Im et al., 2009) suggested that the self-pulsation frequency was almost constant as the recess length increased, whereas according to Kang's experiments (Kang et al., 2016a), the self-pulsation frequency increased first, before decreasing.

As depicted in Fig. 2, there are two independent unstable waves on the gas-liquid interface: sinuous wave and varicose wave (Squire, 1953). Researchers have indicated that the sinuous wave creates a large amplitude on the liquid sheet, whereas the varicose wave is responsible for the primary breakup of the liquid sheet (Mitra et al., 2001). The primary breakup of conical liquid sheets in the axial direction has been widely investigated (Dasgupta et al., 2019; Fu et al., 2010; Lin, 2003). Breakup in the azimuthal direction, however, is usually neglected. Few researchers have addressed the problem of the effect of recess length on the primary breakup of a liquid sheet, especially during self-pulsation. It is difficult to manage experimental access to capture the primary breakup process despite transparent injectors (Matas et al., 2014; Xiao et al., 2018) because the liquid sheet in some cases breakups inside the recess chamber. While numerical studies are easier to perform. Numerical methods have been proved to be a powerful tool in capturing flow dynamics of different injectors (Loureiro et al., 2020; Ridolfi and Folgarait, 2020; Xiao et al., 2016). However, only a section of the injector was simulated in these researches, and several limitations may introduced (Wang et al., 2019). In summary, a three-dimensional simulation to investigate the self-pulsation features of an LCSC injector is necessary.

This study comprehensively investigates the three-dimensional self-pulsation characteristics of LCSC injectors with different recess lengths (Fig. 3). First, self-pulsation features (e.g., spray pattern, primary breakup, characteristic frequency, spray angle) and primary breakup of liquid sheet are analyzed. Then, the flow patterns, pressure oscillations, and flow dynamics are studied. Finally, the self-pulsation mechanism is clarified.