Validation of a Compressible Interfacial Flow Solver Using Jet in Crossflow

An important aspect of scramjet development is characterizing liquid jet atomization in supersonic crossflow under startup conditions. Numerical simulations may be used to better understand the flow behavior. To this end, an interface reconstruction approach extended from a Tangent of Hyperbola for INterface Capturing (THINC) reconstruction scheme for use with the five-equation model has been developed. Coupled with a Harten-Lax-van Leer-Contact (HLLC) Riemann solver–modified to include the effects of surface tension–this method maintains the thickness of the gas-liquid interface throughout the simulation without impacting the underlying conservation of the scheme. The atomization of a liquid jet in subsonic crossflow is simulated and validated against experimental results to ensure the relevant flow physics are captured accurately. A qualitative analysis of the overall flow structure and quantitative comparisons to measured values of liquid jet atomization are performed, including: surface wavelengths, penetration height, and jet trajectory. After examining the subsonic case, a liquid jet in supersonic crossflow is simulated to demonstrate the strength of the method for compressible atomization applications. ∗Corresponding Author: jregele@iastate.edu Introduction Challenges currently exist during scramjet startup conditions when liquid fuel is injected into a supersonic crossflow. As experimental tests are often limited in their ability to observe all of the relevant flow physics, numerical simulation can provide useful insights to the understanding of such flows. Abundant literature exists on the simulation of low Mach number primary atomization, typical to that of a majority of combustion applications. However, little work on the simulation of primary atomization in supersonic conditions has been completed with the effects of liquid surface tension. The development and validation of a numerical model suitable for primary atomization in supersonic flows is vital to further the understanding of the processes involved in supersonic atomization. The method presented utilizes an interface capturing approach which parallels shock capturing schemes already commonly used in compressible flow algorithms [1, 2, 3, 4]. Such an approach is straightforward to implement in compressible solvers and easily extends to multiple dimensions without the need for complex geometric calculations. However, a major drawback of such an approach is the smearing of material interfaces over time similar to contact discontinuities in a compressible solver. A number of techniques have been presented to prevent or reduce interface smearing. One approach is to use WENO [4] or other high order methods with less numerical diffusion. However, such an approach still suffers from interface diffusion over long simulation times. Alternatively, interface compression methods, such as the one presented by Shukla [5], provide another approach. These approaches are often not discretely conservative or must be tailored specifically for the numerical scheme and discretization employed. Another method is the Tangent of Hyperbola for INterface Capturing (THINC) reconstruction method [6]. This approach reconstructs the material interface assuming a locally hyperbolic profile within cells that contain the interface. This method was extended to ρ–THINC in previous work where a similar approach is followed in the reconstruction for the phasic densities [7]. The approach results in a method that is discretely conservative and can maintain the interface thickness to a mesh representable profile through time. The goal of this work is to validate the solver against experimental results for a liquid jet in crossflow. Previous work has shown good agreement of the solver for a variety of test cases as presented in Garrick et al.[7]. Although supersonic atomization is the focus of the solver, regions of subsonic flow are expected behind the bow shock in front of the jet in supersonic conditions. Furthermore a sizable body of literature has been generated on the simulation of liquid jets in subsonic crossflow providing a baseline for comparison [8, 9, 10]. A number of subsonic and supersonic liquid jet experimental results are available in the literature [11, 12, 13]. Among this body of work a wide variety of conditions have been studied: non-turbulent [11, 12], turbulent [14], pulsed [15], and injection direction [16], among others. The large number of parameters can result in a number of uncertainties when attempting to replicate a given experiment in a numerical simulation. Furthermore, significant differences in both simulations [8, 9] and experiments [17] resulting from a slight changes in inflow parameters can be seen, and often such parameters are not completely quantified in experimental results. These can require additional inflow domain simulation or imposing boundaries based on an a priori simulation. A non-turbulent round jet in crossflow was selected to reduce the uncertainty in replicating experimental results for validation. For this work comparisons are made to the work of Wu et al. [11] and Sallam et al. [12]. Wu et al. looked at a number of correlations for non-turbulent round jets and investigated parameters including jet trajectory and break-up lengths. Sallam et al. expanded on this and carefully worked to reduce experimental uncertainty by minimizing the crossflow boundary layer as well as providing additional correlations to experimental data including surface instability wavelengths. The remainder of this paper is organized as follows. First, a discussion of the governing equations and numerical approach is presented. This is followed by the methodology of the recently extended ρ–THINC used to counter the effects of numerical diffusion on the material interface. A validation of the solver is then performed on a liquid jet in subsonic crossflow comparing against experimental data of non-turbulent round jets. Finally the capabilities of the solver for compressible atomization are demonstrated in the simulation of a liquid jet in supersonic crossflow. Governing Equations For the problem considered, the compressible multicomponent Navier-Stokes equations with capillary force terms govern the fluid flow. The five equation model of Allaire [3] is employed to model the given two-fluid problem: