Numerical Simulation of Aerated-Liquid Injection into a Supersonic Crossflow

Numerical simulations of an aerated-liquid jet in a Mach 1.94 crossflow are presented. The numerical method includes solving the Reynold’s averaged Navier-Stokes (RANS) equations with the shear stress transport (SST) turbulence model coupled to a Lagrangian droplet tracker to simulate the structures of the discharged plumes. Effects of turbulent dispersion and secondary break-up are considered. A simplified injection model is proposed where a spherical cone is used to specify the injection region given user specified spray angle, mean droplet diameter, and droplet size distribution. To compare with available experimental data, water is chosen as the liquid for each case. A grid refinement study was conducted to determine appropriate resolutions. Comparisons are made to phase Doppler particle analyzer (PDPA), shadowgraph, and laser-sheet imaging. Results suggest reasonable agreement between the chosen model conditions and the experimental data available. Particular attention is made to consider the biases within each experimental technique and how to best evaluate the simulated results with these considerations in mind. __________________________________________ Corresponding author, brett.bornhoft.1@us.af.mil Introduction Liquid jets in crossflows are important in several applications. These flow fields can be found in propulsion systems, agricultural sprays, and painting sprays. Aerated-liquid injection is a subset of injection strategies that preconditions the liquid by injecting small amounts of gas upstream of the nozzle’s injection location within a specificallydesigned injector body. This small amount of gas mixes with the liquid to create two-phase structures prior to discharge. It has been shown in Ref. [1] that the discharged two-phase flows are capable of delivering favorable plume characteristics, such as increased penetration height, enhanced atomization, and a widened the spray plume. A few different approaches to modeling liquid jets in crossflows have been proposed. These include, but are not limited to, the Eulerian-Eulerian approach, where the dispersed and continuous phases are expressed and solved in a Eulerian framework [2, 3], the mixture model, where a volume fraction represents the percentage of liquid and/or vapor residing in each cell [4], or the Eulerian-Lagrangian method, where the continuous phase is solved in the Eulerian framework and the dispersed phase is solved in the Lagrangian framework through the injection of Lagrangian droplets [5]. Promising capabilities of the Eulerian-Lagrangian approach in predicting the average properties of sprays in crossflows have been demonstrated in the Refs. [6, 7]. A significant challenge in modeling an aerated-liquid jet in a crossflow is the injector exit’s boundary condition. Through the experimental efforts of Lin et al. it was observed that the aerated-injector’s nozzle exit yields a core-annular flow structure [8]. This was further analyzed through high resolution simulations that utilized interface capturing techniques to better understand the two-phase flow field [9]. These efforts motivated a set of derivations by Lin et al. that characterize the one dimensional properties of the aerated-injectors across the nozzle region [10]. These derivations assumed a well-mixed two-phase flow and exclusively utilized x-ray fluorescence data and nozzle geometry to calculate gas, liquid, and mixture properties of density, velocity, volume fraction, pressure, and Mach number. It was found that the compressible two-phase flow at the nozzle exit can be choked for an injection condition requiring a high injection pressure. Based on this observation, the two-phase flow condition at the nozzle exit can probably be reasonably modelled without details of the two-phase flows within an aerated-liquid injector. Therefore, assuming a choked flow, it is possible to specify the pressure, temperature, and velocity of the droplets at the injector exit plane given a specified liquid mass flow-rate (?̇?L), gas-to-liquid mass ratio (GLR), and temperature of the incoming mixture. This simplified approach, proposed by Kim et al. [11], yields reasonable injection conditions as compared to results proposed by [9] where the entire injector is simulated in an ILES framework. Unfortunately, information regarding injector spray angle and droplet sizes are not calculable using this method and in the context of this paper must be selected via alternative methods. In the present study, we propose the use of the Eulerian-Lagrangian method to simulate an aeratedliquid jet injected into a supersonic crossflow environment with efforts to model the nozzle exit flows using relevant information provided by previous measurements. Measurements within the discharged liquid plumes, including, shadowgraph images, laser-sheet images, and phase Doppler particle analyzer (PDPA), will be used to valid the present numerical simulations. Experimental Methods Experiments were conducted in Research Cell 19 (RC19) at the Air Force Research Laboratory (AFRL), Wright-Patterson Air Force Base. An aerated-liquid injector was flush mounted to the bottom floor of the high-speed tunnel. The facility is a continuous-run open-loop rectangular supersonic wind tunnel. A complete description and characterization of the tunnel was presented by Gruber et al. [12]. Rectangular windows give visualization access to both the side and top walls of the tunnel. The test section has a height of 127 mm, a width of 152 mm, and a length of 762 mm. Stagnation conditions were set at 206.8 kPa (30 psia) and 260 C (500 F). A supersonic nozzle with a performance Mach number of 1.94 supplies the supersonic air stream. The aerated-liquid injector uses an outside-in aerating scheme where the gas is injected into the liquid crossflow through 16 pairs of aerating orifices located along the mixing chamber of the injector. The injector’s internal mixing chamber diameter is 2.0 mm (0.08 in). A nozzle adapter with a smooth contour is attached to reduce the 2.0 mm diameter to 1.0 mm. It has a length to diameter ratio of 10.0. Figure 1 shows the schematic of the injector. Water and aerating gas were supplied into the aerated-liquid injector at desired flow rates to form the liquid jet. For the case considered here the liquid mass flow rate (mL) is held at 18.2 g/s with a gas-to-liquid mass ratio (GLR) of 4%. Three types of diagnostics were used to characterize the spray structures. A conventional shadowgraph imaging setup with a high-speed camera was used to capture details of the temporal evolution of the liquid plume as well as the penetration height of the plume. A two-component PDPA was also used to determine the properties of the droplets and the spray plume. Details of this technique can be found in Ref. [13]. Droplet size, velocity, number density, and volume flux were measured at a distance of 100 diameters downstream of the injector (x do ⁄ ). These measurements were done on the cross-section (Y-Z) plane normal to the freestream direction (X) to get cross-sectional structures of the spray plume. Lastly, laser sheet imaging was used to look at instantaneous cross-sectional structures of the spray plume at several x do ⁄ locations. These images qualitatively characterize regions of the spray with large amounts of interfacial surface area. Each of these techniques has its own limitations and biases in depicting an optically dense spray. Nonetheless, these measurements will be used together in the present study in order to have a better understanding of the entire plume structure.