The Impacts of Three Flamelet Burning Regimes in Nonlinear Combustion Dynamics

Axisymmetric simulations of a liquid rocket engine are performed using a delayed detached-eddy-simulation (DDES) turbulence model with the Compressible Flamelet Progress Variable (CFPV) combustion model. Three different pressure instability domains are simulated: completely unstable, semi-stable, and fully stable. The different instability domains are found by varying the combustion chamber and oxidizer post length. Laminar flamelet solutions with a detailed chemical mechanism are examined. The $\beta$ Probability Density Function (PDF) for the mixture fraction and Dirac $\delta$ PDF for both the pressure and the progress variable are used. A coupling mechanism between the Heat Release Rate (HRR) and the pressure in an unstable cycle is demonstrated. Local extinction and reignition is investigated for all the instability domains using the full S-curve approach. A monotonic decrease in the amount of local extinctions and reignitions occurs when pressure oscillation amplitude becomes smaller. The flame index is used to distinguish between the premixed and non-premixed burning mode in different stability domains. An additional simulation of the unstable pressure oscillation case using only the stable flamelet burning branch of the S-curve is performed. Better agreement with experiments in terms of pressure oscillation amplitude is found when the full S-curve is used.Comment: 25 pages, 12 figures. Submitted to Combustion and Flame for a Special Issu

Transient Behavior near Liquid-Gas Interface at Supercritical Pressure

Numerical heat and mass transfer analysis of a configuration where a cool liquid hydrocarbon is suddenly introduced to a hotter gas at supercritical pressure shows that a well-defined phase equilibrium can be established before substantial growth of typical hydrodynamic instabilities. The equilibrium values at the interface quickly reach near-steady values. Sufficiently thick diffusion layers form quickly around the liquid-gas interface (e.g., 3-10 microns for the liquid phase and 10-30 microns for the gas phase in 10-100 microseconds), where density variations become increasingly important with pressure as mixing of species is enhanced. While the hydrocarbon vaporizes and the gas condenses for all analyzed pressures, the net mass flux across the interface reverses as pressure is increased, showing that a clear vaporization-driven problem at low pressures may present condensation at higher pressures. This is achieved while heat still conducts from gas to liquid. Analysis of fundamental thermodynamic laws on a fixed-mass element containing the diffusion layers proves the thermodynamic viability of the obtained results.Comment: Submitted for publication in International Journal of Heat and Mass Transfer. 29 pages, 18 figure

Understanding liquid-jet atomization cascades via vortex dynamics

Temporal instabilities of a planar liquid jet are studied using direct numerical simulation (DNS) of the incompressible Navier-Stokes equations with level-set (LS) and volume-of-fluid (VoF) surface tracking methods. $\lambda_2$ contours are used to relate the vortex dynamics to the surface dynamics at different stages of the jet breakup, namely, lobe formation, lobe perforation, ligament formation, stretching, and tearing. Three distinct breakup mechanisms are identified in the primary breakup, which are well categorized on the parameter space of gas Weber number ($We_g$) versus liquid Reynolds number ($Re_l$). These mechanisms are analyzed here from a vortex dynamics perspective. Vortex dynamics explains the hairpin formation, and the interaction between the hairpins and the Kelvin-Helmholtz (KH) roller explains the perforation of the lobes, which is attributed to the streamwise overlapping of two oppositely-oriented hairpin vortices on top and bottom of the lobe. The formation of corrugations on the lobe front edge at high $Re_l$ is also related to the location and structure of the hairpins with respect to the KH vortex. The lobe perforation and corrugation formation are inhibited at low $Re_l$ and low $We_g$ due to the high surface tension and viscous forces, which damp the small scale corrugations and resist hole formation. Streamwise vorticity generation - resulting in three-dimensional instabilities - is mainly caused by vortex stretching and baroclinic torque at high and low density ratios, respectively. Generation of streamwise vortices and their interaction with spanwise vortices produce the liquid structures seen at various flow conditions. Understanding the liquid sheet breakup and the related vortex dynamics are crucial for controlling the droplet size distribution in primary atomization.Comment: Submitted for publication in Journal of Fluid Mechanics. 56 pages; 52 figure

Length-scale cascade and spread rate of atomizing planar liquid jets

The primary breakup of a planar liquid jet is explored via direct numerical simulation (DNS) of the incompressible Navier-Stokes equation with level-set and volume-of-fluid interface capturing methods. PDFs of the local radius of curvature and the local cross-flow displacement of the liquid-gas interface are evaluated over wide ranges of the Reynolds number ($Re$), Weber number ($We$), density ratio and viscosity ratio. The temporal cascade of liquid-structure length scales and the spread rate of the liquid jet during primary atomization are analyzed. The formation rate of different surface structures, e.g. lobes, ligaments and droplets, are compared for different flow conditions and are explained in terms of the vortex dynamics in each atomization domain that we identified recently. With increasing $We$, the average radius of curvature of the surface decreases, the number of small droplets increases, and the cascade and the surface area growth occur at faster rates. The spray angle is mainly affected by $Re$ and density ratio, and is larger at higher $We$, at higher density ratios, and also at lower $Re$. The change in the spray spread rate versus $Re$ is attributed to the angle of ligaments stretching from the jet core, which increases as $Re$ decreases. Gas viscosity has negligible effect on both the droplet-size distribution and the spray angle. Increasing the wavelength-to-sheet-thickness ratio, however, increases the spray angle and the structure cascade rate, while decreasing the droplet size. The smallest length scale is determined more by surface tension and liquid inertia than by the liquid viscosity, while gas inertia and liquid surface tension are the key parameters in determining the spray angle.Comment: Submitted for publication to International Journal of Multiphase Flow. 37 pages; 33 figure

Compressible Flow at High Pressure with Linear Equation of State

Compressible flow varies from ideal-gas behavior at high pressures where molecular interactions become important. Density is described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and pressure, based on two parameters, A and B, related to intermolecular attraction and repulsion, respectively. Assuming small variations from ideal-gas behavior, a closed-form solution is obtained that is valid over a wide range of conditions. An expansion in these molecular-interaction parameters simplifies relations for flow variables, elucidating the role of molecular repulsion and attraction in variations from ideal-gas behavior. Real-gas modifications in density, enthalpy, and sound speed for a given pressure and temperature lead to variations in many basic compressible flow configurations. Sometimes, the variations can be substantial in quantitative or qualitative terms. The new approach is applied to choked-nozzle flow, isentropic flow, nonlinear-wave propagation, and flow across a shock wave, all for the real gas. Modifications are obtained for allowable mass-flow through a choked nozzle, nozzle thrust, sonic wave speed, Riemann invariants, Prandtl's shock relation, and the Rankine-Hugoniot relations. Forced acoustic oscillations can show substantial augmentation of pressure amplitudes when real-gas effects are taken into account. Shocks at higher temperatures and pressures can have larger pressure jumps with real-gas effects. Weak shocks decay to zero strength at sonic speed. The proposed framework can rely on any cubic equation of state and be applied to multicomponent flows or to more-complex flow configurations.Comment: 63 pages, 12 Figure

Flame spread across liquid pools

For flame spread over liquid fuel pools, the existing literature suggests three gravitational influences: (1) liquid phase buoyant convection, delaying ignition and assisting flame spread; (2) hydrostatic pressure variation, due to variation in the liquid pool height caused by thermocapillary-induced convection; and (3) gas-phase buoyant convection in the opposite direction to the liquid phase motion. No current model accounts for all three influences. In fact, prior to this work, there was no ability to determine whether ignition delay times and flame spread rates would be greater or lesser in low gravity. Flame spread over liquid fuel pools is most commonly characterized by the relationship of the initial pool temperature to the fuel's idealized flash point temperature, with four or five separate characteristic regimes having been identified. In the uniform spread regime, control has been attributed to: (1) gas-phase conduction and radiation; (2) gas-phase conduction only; (3) gas-phase convection and liquid conduction, and most recently (4) liquid convection ahead of the flame. Suggestions were made that the liquid convection was owed to both vuoyancy and thermocapillarity. Of special interest to this work is the determination of whether, and under what conditions, pulsating spread can and will occur in microgravity in the absence of buoyant flows in both phases. The approach we have taken to resolving the importance of buoyancy for these flames is: (1) normal gravity experiments and advanced diagnostics; (2) microgravity experiments; and (3) numerical modelling at arbitrary gravitational level

Volume-of-Fluid computational foundation for variable-density, two-phase, supercritical-fluid flows

A two-phase, low-Mach-number flow solver is proposed for compressible liquid and gas with phase change. The interface is tracked using a split Volume-of-Fluid method, which solves the advection of the liquid phase. This split advection method is generalized for the case where the liquid velocity is not divergence-free and both phases exchange mass across the interface, as happens at near-critical and supercritical pressure conditions. In this thermodynamic environment, the dissolution of lighter gas species into the liquid phase is enhanced and vaporization or condensation can occur simultaneously at different locations along the interface. A sharp interface is identified with a Piecewise Linear Interface Construction (PLIC). Mass conservation to machine-error precision is achieved in the limit of incompressible liquid, but not with the liquid compressibility and mass exchange. The numerical cost of solving two-phase, supercritical flows is very high because: a) local phase equilibrium is imposed at each interface cell to determine the interface solution (e.g., temperature); b) a complete thermodynamic model is used to obtain fluid properties; and c) phase-wise values for certain variables (i.e., velocity) are obtained via extrapolation techniques. Furthermore, the Volume-of-Fluid method and the PLIC add extra computational costs. To alleviate this numerical cost, the pressure Poisson equation (PPE) is split into a constant-coefficient implicit part and a variable-coefficient explicit part. Thus, a Fast Fourier Transform (FFT) method can be used to solve the PPE. Various validation tests are performed to show the accuracy and viability of the present approach. Then, the growth of surface instabilities in a binary system composed of liquid n-decane and gaseous oxygen at supercritical pressures for n-decane are analyzed. Other features of supercritical liquid injection are also shown.Comment: 52 pages, 19 figure