arXiv subjects

William A. Sirignano

Publications and source records attributed to William A. Sirignano.

31 records · Page 2Linked to original sources

arXiv2021

Three-dimensional, Rotational Flamelet Closure Model with Two-way Coupling

A new flamelet model is developed for sub-grid modeling and coupled with the resolved flow for turbulent combustion. The model differs from current models in critical ways. (i) Non-premixed flames, premixed flames, or multi-branched flame structures are determined rather than prescribed. (ii) The effects of shear strain and vorticity are determined. (iii) The strain rates and vorticity applied at the sub-grid level are directly determined from the resolved-scale strain rates and vorticity without a contrived progress variable. (iv) The flamelet model is three-dimensional . (v) The effect of variable density is addressed. Solutions to the multicomponent Navier-Stokes equations governing the flamelet model are obtained. By coordinate transformation, a similar solution is found for the model, through a system of ordinary differential equations. Vorticity creates a centrifugal force on the sub-grid counterflow that modifies the molecular transport rates and burning rate. Sample computations of the rotational flamelet model without coupling to the resolved flow are presented first to demonstrate the importance of the new features. Scaling laws are presented for relating strain rates and vorticity at the sub-grid level to quantities at the resolved-flow level for coupling with large-eddy simulations or Reynolds-averaged flows. The time-averaged behavior of a simple turbulent flow is resolved with coupling to the rotational flamelet model. Specifically, a two-dimensional, multicomponent, time-averaged planar shear layer with variable density and energy release is employed using a mixing-length description for the eddy viscosity. Needs for future study are identified.

physics.flu-dyn↗

arXiv2021

Combustion Instability of a Multi-injector Rocket Engine Using the Flamelet Progress Variable Model

The combustion instability is investigated computationally for a multi-injector rocket engine using the flamelet progress variable (FPV) model. A C++ code is developed based on OpenFOAM 4.0 to apply the combustion model. Flamelet tables are generated for methane/oxygen combustion at the background pressure of $200$ bar using a 12-species chemical mechanism. A power law is determined for rescaling the reaction rate for the progress variable to address the pressure effect. The combustion is also simulated by the one-step-kinetics (OSK) method for comparison with the FPV approach. A study of combustion instability shows that a longitudinal mode of $1500$ Hz and a tangential standing wave of $2500$ Hz are dominant for both approaches. While the amplitude of the longitudinal mode remains almost the same for both approaches, the tangential standing wave achieves a larger amplitude in the FPV simulation. A preliminary study of the resonance in the injectors, which is driven by the longitudinal-mode oscillation in the combustion chamber, is also presented.

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arXiv2020

Neural Network Flame Closure for a Turbulent Combustor with Unsteady Pressure

In this paper, neural network (NN)-based models are generated to replace flamelet tables for sub-grid modeling in large-eddy simulations of a single-injector liquid-propellant rocket engine. In the most accurate case, separate NNs for each of the flame variables are designed and tested by comparing the NN output values with the corresponding values in the table. The gas constant, internal flame energy, and flame heat capacity ratio are estimated with 0.0506%, 0.0852%, and 0.0778% error, respectively. Flame temperature, thermal conductivity, and the coefficient of heat capacity ratio are estimated with 0.63%, 0.68%, and 0.86% error, respectively. The progress variable reaction rate is also estimated with 3.59% error. The errors are calculated based on mean square error over all points in the table. The developed NNs are successfully implemented within the CFD simulation, replacing the flamelet table entirely. The NN-based CFD is validated through comparison of its results with the table-based CFD.

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arXiv2020

Strain Rate and Pressure Effects on Multi-branched Counterflow Flames

This study presents methane-air counterflow simulations, in computationally efficient similar form, allowing combustible mixtures to flow from one or both directions in order to learn more about multi-branched propagating flame structures (e.g., a triple flame). These structures with both premixed and non-premixed flames are commonly seen in more practical combustion analyses. A range of realistic mass mixture fractions and asymmetric chemical rate laws are examined while avoiding the commonly forced unreal symmetric behavior with one-step second-order kinetics. Moreover, a survey of critical parameters is performed varying pressure and normal strain rate to define the flame structure and detect different characters. Three flames can co-exist if the strain rate is low enough and the pressure is high enough. However, at higher strain rate and/or lower pressure, only one or two flames might be obtained. Negative regions of heat release rate are observed and linked to potential endothermic reactions. With a rich premixed mixture at low strain rates and pressures, high exothermic reactions producing CO$_2$ and H$_2$O, and consuming CO and H$_2$ causes a heat-release-rate peak. Unexpected character of the lean and rich premixed flames is observed, leading to the conclusion that these flames are diffusion-controlled.

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arXiv2020

Two-phase developing laminar mixing layer at supercritical pressures

Numerical analysis of a shear layer between a cool liquid n-decane hydrocarbon and a hot oxygen gas at supercritical pressures shows that a well-defined phase equilibrium can be established. Variable properties are considered with the product of density and viscosity in the gas phase showing a nearly constant result within the laminar flow region with no instabilities. Sufficiently thick diffusion layers form around the liquid-gas interface to support the case of continuum theory and phase equilibrium. While molecules are exchanged for both species at all pressures, net mass flux across the interface shifts as pressure is increased. Net vaporization occurs for low pressures while net condensation occurs at higher pressures. For a mixture of n-decane and oxygen, the transition occurs around 50 bar. The equilibrium values at the interface quickly reach their downstream asymptotes. For all cases, profiles of diffusing-advecting quantities collapse to a similar solution (i.e., function of one independent variable). Validity of the boundary layer approximation and similarity are shown in both phases for Reynolds numbers greater than 239 at 150 bar. Results for other pressures are also taken at high Reynolds numbers. Thereby, the validity of the boundary layer approximation and similarity are expected. However, at very high pressures, the similar one-dimensional profiles vary for different problem constraints.

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arXiv2020

Self-similar solution of a supercritical two-phase laminar mixing layer

Previous works for a liquid suddenly contacting a gas at a supercritical pressure show the coexistence of both phases and the generation of diffusion layers on both sides of the liquid-gas interface due to thermodynamic phase equilibrium. A related numerical study of a laminar mixing layer between the liquid and gas streams in the near field of the splitter plate suggests that mass, momentum and thermal diffusion layers evolve in a self-similar manner at very high pressures. In this paper, the high-pressure, two-phase, laminar mixing-layer equations are recast in terms of a similarity variable. A liquid hydrocarbon and gaseous oxygen are considered. Freestream conditions and proper matching conditions at the liquid-gas interface are applied. To solve the system of equations, a real-fluid thermodynamic model based on the Soave-Redlich-Kwong equation of state is selected. A comparison with results obtained by directly solving the laminar mixing-layer equations shows the validity of the similarity approach applied to non-ideal two-phase flows. Even when the gas is hotter than the liquid, condensation can occur at high pressures while heat conducts into the liquid. Finally, a generalized correlation is proposed to represent the evolution of the mixing layer thickness for different problem setups.

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arXiv2020

Mixing and Combustion in a Laminar Shear Layer with Imposed Counterflow

Three-dimensional laminar flow structures with mixing, chemical reaction, normal strain, and shear strain qualitatively representative of turbulent combustion at the small scales are analyzed. A mixing layer is subjected to counterflow in the transverse y- and z-directions. Both non-reactive and reactive flows are examined. Reduction of the three-dimensional boundary-layer equations to a one-dimensional similar form is obtained allowing for heat and mass diffusion with variations in density and properties. In steady configurations, a set of ODEs governs the three velocity components as well as the scalar-field variables. A flamelet model for individual diffusion flames with combined shear and normal strain is developed. Another model with solution in similar form is obtained for a configuration with a dominant diffusion flame and a weaker fuel-rich premixed flame. Results for the velocity and scalar fields are found for ranges of Damkohler number Da, normal strain rate due to the counterflow, streamwise-velocity ratio across the mixing layer, Prandtl number, and Mach number. For the flamelet model, a conserved scalar is cast as the independent variable to give an alternative description of the results. The imposed normal strain decreases mixing-layer thickness and increases scalar gradients and transport rates. There is indication of diffusion control for partially premixed flames in the multi-branched flame situation. The enhancement of the mixing and combustion rates by imposed normal strain on a shear layer can be very substantial. Also, the imposition of shear strain and thereby vorticity on the counterflow can be substantial indicating the need for flamelet models with both shear strain and normal strain.

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arXiv2018

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.

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arXiv2018

Dynamics of a spatially developing liquid jet with slower coaxial gas flow

A three-dimensional round liquid jet within a low-speed coaxial gas flow is numerically simulated and explained via vortex dynamics ($λ_2$ method). The instabilities on the liquid-gas interface reflect well the vortex interactions around the interface. Certain key features are identified for the first time. Two types of surface deformations are distinguished, which are separated by a large indentation on the jet stem: First, those near the jet start-up cap are encapsulated inside the recirculation zone behind the cap. These deformations are directly related to the dynamics of the growing cap and well explained by the vortices generated there. Second, deformations occurring farther upstream of the cap are mainly driven by the Kelvin-Helmholtz (KH) instability at the interface. Three-dimensional deformations occur in the vortex structures first, and the initially axisymmetric KH vortices deform and lead to several liquid lobes, which stretch first as thinning sheets and then either continue stretching directly into elongated ligaments - at lower relative velocity - or perforate to create liquid bridges and holes - at higher relative velocity. The different scenarios depend on Weber and Reynolds numbers based on the relative gas-liquid velocity as was found in the temporal studies. The deformations in the upstream region are well portrayed in a frame moving with the convective velocity of the liquid jet. The usefulness of the temporal analyses are now established.

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arXiv2018

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.

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arXiv2018

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 $β$ Probability Density Function (PDF) for the mixture fraction and Dirac $δ$ 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.

physics.flu-dyn↗

arXiv2018

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. $λ_2$ 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.

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arXiv2017

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.

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