Effect of inlet mass flow rate oscillation on simplex swirl injector flow based on VOF-to-DPM model
Introduction
Combustion instability is the result of nonlinear coupling among flame, flow field, and sound field. It increases the vibration of the spacecraft and deteriorates the load environment as well as heat transfer characteristics, which directly threatens the performance and service life of the liquid rocket engine [1]. During the combustion, the periodic oscillation of sound and pressure in the chamber will be transmitted to the supply system through the injectors, and the pressure fluctuation in the supply system will cause the flow oscillation of the propellant entering the injector. The oscillation of inlet propellant flow will affect the outlet flow rate, pressure, and spray characteristics of the injector [2]. Intense outlet flow rate and pressure oscillation, bigger spray cone angle, and smaller droplets may lead to combustion instability [3,4]. Hence, inlet propellant oscillations of the injector have a significant impact on combustion instability. And there is an urgent need to study the flow characteristics (including response and spray characteristics) of the injector under the oscillations. Response characteristic is usually analyzed by amplitude ratio and phase angle between the inlet and outlet oscillations, which can be used to infer whether the inlet and outlet oscillations promote each other. Spray characteristics are presented by the diameter of the droplets, and the flow field in the paper.
To explore the response characteristics of the injector, many scholars have studied the effect of inlet oscillation with different frequencies theoretically. Bazarov et al. [2] derived the expression of the dynamic transfer function of the simplex swirl injector by linear theoretical analysis, obtained the linear frequency response characteristics of the swirl injector in a wide frequency range, and were able to predict the change criteria of the mass flow rate at the injector orifice with different-frequency inlet oscillation. Yang and Fu based on Bazarov's theory, and considered operation conditions and structural parameters when deriving the transfer function of the swirl injector. They illustrated that operation conditions impact greatly the oscillation of the injector outlet and had many accomplishments in injector dynamics [[5], [6], [7], [8], [9], [10], [11]]. While some remarkable achievements have been made in theoretical analysis, which can analyze the responsive amplitude and phase difference of the injector but cannot further explore the effect of inlet flow oscillation on spray characteristics. However, spray characteristics, such as bigger spray angles and smaller droplets probably provoke combustion instability. To get a better understanding of the injector with oscillation, other scholars have carried out experimental research about the effect of different-frequency oscillation on spray cone angle and liquid film thickness. Ahn et al. [12] generated inlet frequencies ranging from 0 to 500 Hz experimentally and found the spray cone angle of the injector oscillated more intensely at the frequency of 200–300 Hz. Chung et al. [13] measured outlet pressure and the liquid film thickness. They opined that the oscillation amplitude of the liquid film thickness reaches the maximum at 200 Hz without regard to differences in the swirl chamber's length and diameter. Yang et al. [14] investigated the response characteristics of the liquid film and atomization fluctuations experimentally. They believed that the sensitive frequency range of the injector is 100–200 Hz. Meanwhile, they proposed that the liquid film has a low-pass filtering effect so that the atomization can only respond to pressure oscillations less than 300 Hz. Xue et al. [15] used an analogous experimental method to find that the liquid film is sensitive to the oscillation of the long wave, while impervious to the shorter wave. The experiment can study the effect of inlet mass flow oscillation on outlet pressure under the interferences of the flow field, and obtain time-averaged spray angle and liquid film thickness to find out the sensitive frequency. But it cannot acquire transient flow at the orifice, instant droplet size, and flow field distribution because of limitations in equipment. Outlet flow, instant droplets, and flow field distribution are essential to combustion instability as well.
According to experimental and theoretical analysis, neither experiment nor theoretical analysis can concurrently acquire complete response and spray characteristics under different oscillations. Since combustion instability is such a sophisticated coupling process that is related to both response and spray characteristics. Studying response and spray characteristics as much as possible is vital to reveal the mechanism of combustion instability and reduce the probability of combustion instability by active flow regulations. Simulation has the characteristics of strong operability with more measurable information, which can describe the whole spray process inside and outside the injector without the limitations of experimental devices and flow field interference. Thus, it can monitor outlet pressure, mass flow, and droplets diameters as well as the velocity distribution of the flow field in time. In terms of atomization simulation, the commonly used liquid phase volume method (VOF) can calculate the liquid breakup process, but capturing the droplets requires burdensome mesh. And the discrete phase model (DPM) can describe the droplet trajectory on a larger mesh, but cannot simulate the liquid breakup process. On the premise of the computational cost, it is always arduous to acquire both liquid breakup and droplet information. The VOF-to-DPM model combines the advantages of the VOF method which can calculate the breakup of continuous liquid and the DPM model which can capture the droplet trajectory on a larger grid. Hence, the VOF-to-DPM model has been applied to emulate the whole atomization process. Zhou et al. [16] based on the VOF-to-DPM model and grid adaptive technology, depicted the liquid/liquid spray process of a pintle injector. Wang et al. [17] applied large eddy simulation to reveal the phenomenon of the interface flow in the injector and the breakup of the external liquid film by coupling VOF and DPM. They also obtained the droplet size of the injector as well. Xu et al. [18] utilized the VOF-to-DPM model to accurately simulate the formation of the liquid film of the swirl injector, the transversion of the liquid film from primary breakup to the secondary atomization, and producing droplets. The spray angle obtained by simulation is consistent with which measured by the experiment. The above-reported work indicates that the VOF-to-DPM model is capable to simulate the whole process of atomization.
Swirl coaxial injectors are commonly preferred in liquid rocket engines [19]. The simplex swirl injector with the annular channel is typical and vital for both liquid-liquid swirl coaxial injectors and gas-center swirl coaxial injectors but is seldom paid attention to Ref. [20]. At present, a few simulations focus on the simplex swirl injector's amplitude and phase characteristics and do not associate them with the flow field. In addition, compared to other injectors, the simplex swirl injector has more theoretical and experimental achievements, which facilitates the verification of the proposed method. The proposed method is successfully applied to simple and typical injectors first and will be followed by swirl coaxial injectors. Obtained results of the simplex swirl injector are also helpful for subsequent research on swirl coaxial injectors. Hence, the paper proposed a method combining the VOF-to-DPM model and inlet mass flow oscillation, which is employed to simulate the internal and external flow field of the simplex swirl injector and acquire a complete response and spray characteristics. The application of the proposed method is of extreme significance for analyzing the relationships between the response and spray characteristics of the injectors, revealing the mechanism of combustion instability and improving the reliability of liquid rocket engines.
The paper is organized as follows. In section 2, the proposed methodology is introduced. In section 3, the injector geometry and numerical model are listed. The numerical conditions and verification as well as grid convergence are carried out in this section as well. Detailed discussions of the effect of inlet mass flow rate oscillation on the injector are provided in section 4. Conclusions are summarized in section 5.
Section snippets
Numerical methodology
The proposed methodology consists of three steps as Fig. 1. First, add the inlet mass flow oscillation function to the simulated cases. Then, the programmed VOF-to-DPM model is applied to the atomization development. Finally, the simulation will end until the calculation time meets the requirements.
Firstly, the inlet mass flow oscillation is the function of flow time. According to the film theory, the instability increases rapidly in a sinusoidal manner [21], based on which the inlet mass flow
Simplex swirl injector geometry
Considering the feasibility of verifying the method, the present study applied Ding's model for simulation. The key geometrical parameters are listed in Table 1 [20]. And the diagram of the injector with corresponding parameters is portrayed in Fig. 2 [20].
Numerical scheme
As shown in Fig. 3, the numerical domain contains the simplex swirl injector with an annual channel and conical region outside the injector. The conical region is 25 mm with an expansion angle of 80°, which is enough to depict the features of
The effects of the oscillation frequency
Fig. 6 depicts variations of inlet mass flow (mi), outlet mass flow (mo), and the outlet total pressure (TP injector orifice) with flow time at different frequencies. The premise for response characteristics is that the inlet and outlet periods are consistent. The simulation periods of outlet mass flow and pressure at 100 Hz, 200 Hz, 300 Hz, 400 Hz, and 500 Hz are about 0.01s, 0.005s, 0.003s, 0.0025s, and 0.002s respectively, which are identical to the periods of the inlet. Therefore, the
Conclusion
The paper has proposed a methodology integrating different frequency-and-amplitude oscillations with the VOF-to-DPM model. The method has investigated the effect of inlet mass flow oscillation on the injector to explore the mechanism of combustion instability. Based on the proposed method, the transient outlet mass flow rate and pressure, the Sauter Mean Diameter of the liquid droplets, and the distribution of the flow field are effectively brought. According to the results, the conclusions
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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