Numerical Simulation of Primary Atomization of Non-Newtonian Impinging Jets

Newtonian impinging jets have been investigated for decades. However, limited is known about non-Newtonian impinging jets. The present work attempts to improve this situation by performing high-fidelity numerical simulations of non-Newtonian impinging jet dynamics. Emphasis is placed on the near field of the liquid sheet formed by the impingement of two shear-thinning (viscosity deceases with increasing shear rate) liquid jets, and the ensuing atomization The formulation is based on a complete set of conservation equations for both the liquid and surrounding gas phases. An improved volume-of-fluid (VOF) method, combined with an innovative topology-oriented adaptive mesh refinement (TOAMR) technique, is developed and implemented to track the interfacial dynamics. The stringent requirements for grid resolution for fine and thin structures are resolved efficiently in the computational domain. Especially, the refinement at the interface to the minimum required grid size is treated effectively to substantially reduce the simulation cost. Results show good agreement with available experimental data in terms of sheet topology and breakup length of the unstable hydrodynamics wave, known as the impact wave. Comparison is made with Newtonian liquid jets to identify the underlying physical mechanisms of jet dynamics, sheet formation, impact waves, and atomization. The work allows for investigation into the evolution of the shear rates in the liquid sheet and at the interface. It is found that the viscosity decreases in the region where the impingement of the two liquid jets results in a high shear rate. Increasing the volume of this low viscosity region can enhance atomization. Information obtained from the present study can be used to optimize the design parameters of non-Newtonian impinging jet injectors, including the impingement angle, jet diameter, and off-center distance of the two jets. ILASS Americas, 25 Annual Conference on Liquid Atomization and Spray Systems, Pittsburgh, PA, May 2013 Introduction Collision of two cylindrical jets is one of the canonical configurations for the generation of liquid sheets. The dynamics and stability of liquid sheets have attracted a great deal of attention due to their relevance to the atomization and combustion processes in liquid rocket engines[1-4]. Impingement is an efficient method for atomizing and mixing the liquid jets. The dynamic head of one of the jets is used to destabilize the opposing jet stream, thereby resulting in fragmentation of the jet into ligaments and droplets [5]. The atomization of impinging jets of Newtonian fluids has been extensively investigated experimentally and theoretically. Dombrowski and Hooper [6] investigated the factors that affect the breakup of sheets and studied wave motions (impact wave) of high velocity liquid sheets. Anderson et. al[7] developed a phenomenological threestep model of atomization including atomization of the impinging jets, and sheet and ligament breakup processes. , provided a good correlation with the experimental data. Theoretical studies have been limited due to the excessive complexity of relevant physical processes. Preliminary works focused on atomization of the impinging jets [8-11]. Recently, Chen et. al[12] performed high-fidelity numerical simulations and investigated phenomena responsible for the formation of the impact wave. The Strouhal number locking-on feature of an impact wave was found to be similar to that observed for perturbed free shear layers, thereby indicating that the flow mechanism of an impact wave is analogous to that of free shear layers[13]. Gelled propellants feature many advantages over non-gelled liquid and solid rocket propellants. They are safe to store and handle and comply with insensitive munitions requirements. The inherent thrust modulation capability provides good application flexibility for utilization in tactical rocket engine. Gelled propellants are non-Newtonian fluids, since their viscosity depends on the shear rate. They are difficult to atomize and require higher injection pressures. As a result, it would be advantageous for the gelled propellants to be shearthinning liquids whose viscosity decreases with increasing shear rate. The formation and breakup mechanisms of non-Newtonian liquid sheets formed by impinging jets are poorly known. Fakhri [14] studied the development and atomization process of non-Newtonian impinging jets of gelled propellant simulants. The physical and rheological properties of gelled simulants are identical to those of conventional hypergolic propellants. Near-field spray characteristics such as the sheet formation and breakup length of the liquid sheet were determined. The droplet size distributions were measured in the far field region downstream of the impingement location. Coil [15] studied the effect of the gel phase on the atomization of impinging jets. The spray behaviors of Newtonian oil and gelled oil were compared using high-speed images. Yang [16] performed a linear instability analysis and predicted the breakup length and wavelength for a non-Newtonian liquid exhibiting power-law behavior. The results were in good agreement with the experimental data. Direct numerical simulation (DNS) can be used to determine the effect of shear-thinning on the atomization process of non-Newtonian liquids. The result can be used to guide the injector design by improving the performance and reducing the required pressure of the supply system The present study focuses on analyzing the atomization process of non-Newtonian impinging jets. Emphasis is placed on physical processes that occur in the vicinity of the impingement location. Theoretical Framework a. Numerical methods Atomization is a complex physical process featuring large density ratios and significant viscous and surface tension forces. It involves dynamic and complex interfacial geometries with length scales spanning several orders of magnitude. An open-source flow solver, GERRIS[17] is employed in the present study. The numerical method [18] combines an adaptive quad/Octree spatial discretisation, geometrical Volume-Of-Fluid interface representation, balanced-force continuumsurface-force surface tension formulation, and heightfunction curvature estimation. It recovers exact equilibrium (to machine accuracy) between surface tension and pressure gradient for the case of a stationary droplet, irrespective of the viscosity and spatial resolution. The three-dimensional incompressible, variable-density conservative equations can be written as ( ) 0 tρ ρ ∂ +∇ ⋅ = u (1) ( ) (2 ) t s p ρ μ σκδ ∂ + ⋅ ∇ = −∇ + ∇ ⋅ + u u u D n (2)