International Journal of Rotating Machinery

Volume 2016 (2016), Article ID 1201497, 11 pages

http://dx.doi.org/10.1155/2016/1201497

## Numerical Investigation on Primary Atomization Mechanism of Hollow Cone Swirling Sprays

School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China

Received 23 December 2015; Revised 27 March 2016; Accepted 10 April 2016

Academic Editor: Sourabh V. Apte

Copyright © 2016 Jia-Wei Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The atomization process of swirling sprays in gas turbine engines has been investigated using a LES-VOF model. With fine grid resolution, the ligament and droplet formation processes are captured in detail. The spray structure of fully developed sprays and the flow field are observed firstly. A central recirculation zone is generated inside the hollow cone section due to the entrainment of air by the liquid sheet and strong turbulent structures promote the breakup of ligaments. At the exit of injector nozzle, surface instability occurs due to disturbance factors. Axial and transverse mode instabilities produce a net-like structure ligament zone. Finally, the generation mechanism of the droplet is analyzed. It is found that the breakup mechanism of ligaments is located at the Raleigh capillary region. Axial symmetry oscillation occurs due to the surface tension force and the capillary waves pinch off from the neck of the ligaments. Secondary breakup and coalescence occur at the “droplet zone,” resulting in a wider distribution curve at the downstream area.

#### 1. Introduction

Liquid atomization is an important process in internal combustion engines. The quality of spray atomization directly affects fuel combustion, which consequently determines engine performance. In gas turbine engines, pressure swirl injectors are widely used because of their good atomization capability and geometrical simplicity [1]. In a pressure swirl injector, liquid is injected through twisty slots; thus tangential velocity is endued to the fluid in orifice and spray cone emerges due to the centrifugal force. The liquid sheet becomes unstable and breaks up into ligaments, and then ligaments break up into droplets and secondary breakup occurs downstream of the spray. The atomization of swirling jet is a complex process that is affected by many factors and its mechanism needs to be understood properly [2].

Over the past several decades, a series of theoretical and experimental investigations have been performed in both industry and academia for a better understanding of the atomization process of swirling jet [3–5]. Ponstein [6] investigated the growth of disturbance of an annular swirling liquid sheet based on instability analysis. In his research, the viscosity of both phases has been neglected. Liao et al. [7] developed a theoretical model to predict the performance of simplex atomizer based on the study of an inviscid, swirling annular liquid sheet. Ibrahim and Jog [8] studied the nonlinear instability and breakup of an annular liquid sheet using a perturbation expansion method, the effect of liquid Weber number, initial disturbance, and gas swirl strength on the breakup characteristics is investigated. So far, the literature on theoretical investigation was based on many simple assumptions and it is difficult to predict the sheet breakup accurately without taking into account the complex interaction between liquid and gas.

Experimentally, studies are carried out to predict the atomization characteristics (spray angle, liquid film breakup length, and drop size distribution) of swirling spray [9–13]. Although there have been many investigations on the spray characteristics of swirling jet, most of them focus on the macroscopic properties of atomization, and investigations on liquid film instability and ligament breakup process are still lacking. Also, to observe the small and dense region where ligaments and droplets occur, high spatiotemporal resolution of visualization technology is needed. So far, the entire breakup mechanism of swirling jet has not been revealed yet by experiment and further investigations are demanded.

In recent years, with the development of interface capturing methods, numerical simulations have been carried out to predict the breakup process of liquid jet. Ménard et al. [15] used coupled level set/VOF/ghost methods to investigate the atomization of a liquid jet injected into still gas. Desjardins et al. [16] applied combined level set/VOF method to the primary breakup of a straight liquid jet. De Villiers et al. [17] used LES-VOF method to investigate the atomization of a round jet influenced by nozzle flow. Herrmann et al. [18–20] discussed the influence of gas/liquid density ratio on liquid jet penetration and the primary breakup characteristics using level set method and fine grid. Shinjo and Umemura [21, 22] performed a detailed numerical simulation of straight liquid jets of diesel fuel. As a result, they were able to characterize ligament generation and surface instability development on the liquid jet core influenced by aerodynamics. Siamas et al. [23] investigated the surface instability and flow field of a swirling annular jet using VOF method, but the simulation only focuses on the region close to the nozzle exit. Using high performance computer system and with fine grid resolution, the ligament and droplet formation process can be captured correctly which is hard to be observed in experiment investigation, allowing a detailed study of liquid atomization mechanism.

In the present study, a volume of fluid (VOF) interface tracking method and a large eddy simulation (LES) model were used for computing the atomization process of swirling sprays. The present research mainly focuses on the breakup process of liquid film and the droplet formation process. The ligament structure and droplet formation mechanism will be identified. The remainder of this paper is organized as follows: Section 2 presents the numerical methodology and the simulation setup procedures. Section 3 presents the numerical results and discussion. Finally, Section 4 presents the concluding remarks.

#### 2. Numerical Method

##### 2.1. Governing Equations

In large eddy simulation, the subgrid structures are modelled while the large eddy turbulent structures are resolved on a computational grid.

In the present model, the simultaneous flow is treated as immiscible, incompressible continuum fluids with an effective viscosity and surface tension. The continuity and momentum equations are as follows:where and are velocities and the subscript , indicated the coordinate () indices, is density, is pressure, is kinetic viscosity, is subgrid scale (SGS) stress, is surface tension, and is the force of gravity.

The surface tension force is represented as a continuous surface force model [24]:where the interface unit normal vector and the curvature of the interface are given by

SGS stress can be approximated by the SGS model. In the present simulation, the Smagorinsky model [25] is used and it can be written aswhere is SGS viscosity, is the constant, and is the Smagorinsky model coefficient of 0.18.

The liquid volume fraction represents the indicator function with for gas and for liquid. The local density and viscosity in a computational cell are given in terms of the liquid volume fraction bywhere subscripts and represent the liquid and gas phases, respectively.

The indicator function obeys a transport equation as follows:

##### 2.2. VOF Scheme

The interface of liquid phase and gas phase can be computed with interface tracking or interface capturing methods. For the interface tracking methods, such as SLIC [26], PLIC [27], and their variations [28], the interfaces are reconstructed using geometric formulations. While for the interface capturing methods (CICSAM [29] and HRIC [30]), algebraic methods are employed to identify the interface locations. In HRIC method, the compressive scheme that is used to avoid the smearing of the interface could lead to interface stepping problem. To remedy this, a switching strategy that switches between compressive and noncompressive scheme called CICSAM was proposed by Ubbink [29]. In the present paper, CICSAM is used to capture the interface of liquid phase and gas phase.

CICSAM is implemented in the framework of* OpenFOAM* [31] as an explicit scheme which uses normalised variable diagram (NVD) and switches among different differencing schemes to furnish a bounded scalar field. Such approach could create an interface which is as sharp as that produced by geometric reconstruction schemes such as piecewise linear interface.

The finite volume discretization of the volume fraction convection equation based on the integral form is as follows:where indicates the center of control volume, is the cell face centroid, and is the the volumetric flux through the cell face.

For a sufficiently small time step, the diversion of on the cell face is negligible, and (7) is reduced towhere is the new volume fraction distribution described as

The weighting factor is given by NVD and can be expressed as

Using the boundedness constraint in the upwind control cell , the normalised variable and are given bywhere , , and are the donor, acceptor, and upwind cells.

The cell face values of are resolved by convection boundedness criteria (CBC). The HYPER-C based normalised variable is given by

The ULTIMATE-QUICKEST-based normalised variable is given bywhere is the local value of Courant number at the face.

Ubbink [29] introduced the following weighting factor to switch smoothly between the less compressive differencing scheme and the upper bound of CBC:

The weighting factor is based on the cosine of the angle between the vector normal to the interface and the vector , which connects the centers of the donor and acceptor cells:where is a constant introduced to control the dominance of different schemes. The recommended value is .

##### 2.3. Numerical Methodology

The employed transient multiphase solver of* OpenFOAM* [31] utilizes a cell center-based finite volume method and provides a comprehensive range of discretization schemes that can be selected for each term in the equations being solved. Crank-Nicholson method with second-order accuracy is used for the time discretion of governing equations. For general field interpolations, a linear form of central differencing scheme is applied. Convective fluxes are discretized with the Gauss linear scheme. Pressure velocity coupling is addressed with the pressure implicit split operator (PISO) algorithm.

##### 2.4. Code Validation

###### 2.4.1. A 2D Droplet Test

To validate the code accuracy in capturing the liquid-gas interface, a test case of a 2D drop is simulated similar to Zheng et al. [14]. In the test case, a drop of radius is located in a square domain of , which is sheared by a gas flow. At the top and bottom of the domain, the tangential velocity is prescribed as and . The right and left sides of the domain are set as velocity inlet and outlet boundary. The velocity of the boundary is given by

Figure 1 shows the shape of the droplet at , and the circular droplet becomes elliptical due to the shear flow. Figure 2 contains the evolution of the half-length of the 2D drop. The result shows good agreement with the value calculated by Zheng et al. [14].