Previously, a theory has been presented that explains how discrete vapor–liquid interfaces become diminished at certain high-pressure conditions in a manner that leads to well known qualitative trends observed from imaging in a variety of experiments. Rather than surface tension forces, transport processes can dominate over relevant ranges of conditions. In this paper, this framework is now generalized to treat a wide range of fuel-oxidizer combinations in a manner consistent with theories of capillary flows and extended corresponding states theory. Different flow conditions and species-specific molecular properties are shown to produce distinct variations of interfacial structures and local free molecular paths. These variations are shown to occur over the operating ranges in a variety of propulsion and power systems. Despite these variations, the generalized analysis reveals that the envelope of flow conditions at which the transition from classical sprays to diffusion-dominated mixing occurs exhibits a characteristic shape for all liquid–gas combinations. As a result, for alkane-oxidizer mixtures, it explains that these conditions shift to higher pressure flow conditions with increasing carbon number and demonstrates that, instead of widely assumed classical spray atomization, diffusion-dominated mixing may occur under relevant high-pressure conditions in many modern devices.
Until recently, modern theory has lacked a fundamentally based model to predict the operating pressures where classical sprays transition to dense-fluid mixing with diminished surface tension. In this paper, such a model is presented to quantify this transition for liquid-oxygen–hydrogen and n-decane–gaseous-oxygen injection processes. The analysis reveals that respective molecular interfaces break down not necessarily because of vanishing surface tension forces but instead because of the combination of broadened interfaces and a reduction in mean free molecular path. When this occurs, the interfacial structure itself enters the continuum regime, where transport processes rather than intermolecular forces dominate. Using this model, regime diagrams for the respective systems are constructed that show the range of operating pressures and temperatures where this transition occurs. The analysis also reveals the conditions where classical spray dynamics persists even at high supercritical pressures. As a result, it demonstrates that, depending on the composition and temperature of the injected fluids, the injection process can exhibit either classical spray atomization, dense-fluid diffusion-dominated mixing, or supercritical mixing phenomena at chamber pressures encountered in state-of-the-art liquid rocket engines.
This study presents a detailed analysis of the flow topologies and turbulence scales in the jet-in-cross-flow experiment of [Su and Mungal JFM 2004]. The analysis is performed using the Large Eddy Simulation (LES) technique with a highly resolved grid and time-step and well controlled boundary conditions. This enables quantitative agreement with the first and second moments of turbulence statistics measured in the experiment. LES is used to perform the analysis since experimental measurements of time-resolved 3D fields are still in their infancy and because sampling periods are generally limited with direct numerical simulation. A major focal point is the comprehensive characterization of the turbulence scales and their evolution. Time-resolved probes are used with long sampling periods to obtain maps of the integral scales, Taylor microscales, and turbulent kinetic energy spectra. Scalar-fluctuation scales are also quantified. In the near-field, coherent structures are clearly identified, both in physical and spectral space. Along the jet centerline, turbulence scales grow according to a classical one-third power law. However, the derived maps of turbulence scales reveal strong inhomogeneities in the flow. From the modeling perspective, these insights are useful to design optimized grids and improve numerical predictions in similar configurations.
Significant inadequacies of current models for multiphase flows present a major barrier to rapid development of advanced high-efficiency low-emissions combustion devices. Liquid spray atomization processes largely determine fuel-air mixture formation, which subsequently govern combustion and controls performance, emissions, and durability of a device. The current study presents a fundamentally-consistent framework to model the effects of breakup processes, liquid drop deformations, and internal flow dynamics on mass, momentum, and energy exchange functions. This framework builds on the Taylor Analogy Breakup (TAB) model which naturally quantifies local drop deformation dynamics. Real-fluid multicomponent thermodynamic property modeling and Gradient Theory simulations facilitate accurate calculations of molecular two-phase interface exchange functions, surface tensions forces, drop oscillations, and breakup processes. The analysis establishes that these drop dynamics, along with finite liquid viscosity effects, significantly alter gas-liquid exchange functions. The study quantifies these effects for the resulting drag coefficients of liquid drops and demonstrates significant deviations from the classic dynamic drag model, which is widely applied in modern simulations performed in academia and industry. This work also quantifies effects, which originate from gas-liquid coupling dynamics, on evaporation and heating rates. The analysis establishes that the consideration of these coupling dynamics modify mass and energy transfer rates even more significantly than the corresponding drag forces from momentum exchange. This physical complexity, however, is largely neglected in modern studies from academia and industry. A new set of equations is presented to improve the modeling of drop breakup processes to address the current shortcomings in the prediction of resulting drops proper- ties over the full range of relevant breakup conditions. The framework is based on a refined energy balance equation which explicitly enforces drop momentum conservation during the breakup process. The introduced modeling framework is entirely derived from conservation equations for mass, momentum, and energy and does not, as a consequence, introduce new modeling constants. The significance of the developed modeling advances to fuel injection processes is demonstrated using Large Eddy Simulation (LES) with a Lagrangian-Eulerian modeling approach.
Large-eddy-simulation (LES) is quickly becoming a method of choice for studying complex thermo-physics in a wide range of propulsion and power systems. It provides a means to study coupled turbulent combustion and flow processes in parameter spaces that are unattainable using direct-numerical-simulation (DNS), with a degree of fidelity that can be far more accurate than conventional engineering methods such as the Reynolds-averaged Navier-Stokes (RANS) approximation. However, development of predictive LES is complicated by the complex interdependence of different type of errors coming from numerical methods, algorithms, models and boundary con- ditions. On the other hand, control of accuracy has become a critical aspect in the development of predictive LES for design. The objective of this project is to create a framework of metrics aimed at quantifying the quality and accuracy of state-of-the-art LES in a manner that addresses the myriad of competing interdependencies. In a typical simulation cycle, only 20% of the computational time is actually usable. The rest is spent in case preparation, assessment, and validation, because of the lack of guidelines. This work increases confidence in the accuracy of a given solution while minimizing the time obtaining the solution. The approach facilitates control of the tradeoffs between cost, accuracy, and uncertainties as a function of fidelity and methods employed. The analysis is coupled with advanced Uncertainty Quantification techniques employed to estimate confidence in model predictions and calibrate model's parameters. This work has provided positive consequences on the accuracy of the results delivered by LES and will soon have a broad impact on research supported both by the DOE and elsewhere.
Kinetic theory is often used as a framework to derive moment equations for sprays, with considerable success in the case of a dilute spray in a fully resolved (DNS) gas field. In the prospect of computing LES of atomization with a spray solver, a formalism that accounts for the non-linear interaction between high-loading regions and turbulence at the subfilter level is needed. So we first introduce a kinetic theory frame, where the phase space is extended to space-filtered spray quantities. This rigorous formalism is a comprehensive baseline but it requires closures. Second we quantify segregation, through a priori DNS, as a relevant space-filtered quantity to account for the spray’s subfilter behavior. Third we discuss an assumption on the subfilter spray structures which allows the closure of drag, heating, and collisions from the sole knowledge of segregation.
The transition of classical spray atomization processes to single-phase continuous dense-fluid mixing dynamics with diminished surface tension forces is poorly understood. Recently, a theory has been presented that established, based on a Knudsen-number criterion, that the development of such mixing layers is initiated because the multicomponent two-phase interface becomes much wider than the mean free molecular path. This shows that the transition to mixing layers occurs due to interfacial dynamics and not, as conventional wisdom had suggested, because the liquid phase has heated up to supercritical temperatures where surface tension forces diminish. In this paper we focus on the dynamics of this transition process, which still poses many fundamental questions. We show that such dynamics are dictated by substantial statistical fluctuations about the average interface molecule number and the presence of significant interfacial free energy forces. The comprehensive analysis is performed based on a combination of non-equilibrium mean-field thermodynamics and a detailed modified 32-term Benedict-Webb-Rubin mixture state equation. Statistical fluctuations are quantified using the generally accepted model of Poisson-distributions for variances in systems with a small number of molecules. Such fluctuations quantify the range of pressure and temperature conditions under which the gradual transition to dense-fluid mixing dynamics occurs. The interface begins to deteriorate as it broadens substantially. The related interfacial free energy forces do not instantly diminish only because vapor-liquid equilibrium conditions do not apply anymore. Instead, such forces along with the present interfacial statistical fluctuations are shown to gradually decrease as the interface transitions through the molecular chaos regime and to diminish once the interface enters the continuum regime. Then, the interfacial region becomes a continuous gas-liquid mixing layer with diminished free energy forces that is significantly affected by single-phase real-fluid thermodynamics and transport properties.
Liquid injection in systems such as liquid rockets where the working fluid exceeds the thermodynamic critical condition of the liquid phase is not well understood. Under some conditions when operating pressures exceed the liquid phase critical pressure, surface tension forces become diminished when the classical low-pressure gas-liquid interface is replaced by a diffusion-dominated mixing layer. Modern theory, however, still lacks a physically-based model to explain the conditions under which this transition occurs. In this paper, we derive a coupled model to obtain a theoretical analysis that quantifies these conditions for general multicomponent liquid injection processes. Our model applies a modified 32-term Benedict-Webb-Rubin equation of state along with corresponding combining and mixing rules that accounts for the relevant thermodynamic non-ideal multicomponent mixture states in the system. This framework is combined with Linear Gradient Theory, which facilitates the calculation of the vapor-liquid molecular structure. Dependent on oxygen and hydrogen injection temperatures, our model shows interfaces with substantially increased thicknesses in comparison to interfaces resulting from lower injection temperatures. Contrary to conventional wisdom, our analysis reveals that LOX-H2 molecular interfaces break down not necessarily because of vanishing surface tension forces, but because of the combination of broadened interfaces and a reduction in mean free molecular path at high pressures. Then, these interfaces enter the continuum length scale regime where, instead of inter-molecular forces, transport processes dominate. Based on this theory, a regime diagram for LOX-H2 mixtures is introduced that quantifies the conditions under which classical sprays transition to dense-fluid jets.
Progress toward application of the Large Eddy Simulation (LES) technique to turbulent multiphase combustion processes typically encountered in advanced propulsion and power systems is presented. The objective is to provide a systematic analysis of current findings and assist in the development of technical performance metrics for model development and validation. Research is currently required to provide both improved multiphase combustion models and improved datasets for validation. Requirements for further model development must be established through detailed analyses of the space-time characteristics of small-scale flame structures and turbulence-chemistry interactions. Concurrently, a refined set of implementation requirements must be established for LES. Steps taken towards these goals are described in the context of a generalized formulation of the filtered conservation equations using an arbitrary filter function that operates on both spatial and temporal scales. Case studies are presented that demonstrate current findings in the treatment of complex thermophysical processes typically present in advanced systems followed by discussion to add perspective on future needs.