arXiv subjects

William A. Sirignano

Publications and source records attributed to William A. Sirignano.

At least 19 recordsLinked to original sources

arXiv2026

Perturbation Theory for Translating Oblate-Spheroidal Droplets with Internal Circulation

Liquid droplets deform from spherical shape due to aerodynamic variation of pressure along the surface as the droplet moves through a gas. The deformation is predicted for axisymmetric droplets translating through a gas with low Weber numbers, We < 1, and Reynolds number Re = O(10). That deformation analysis is based on the relations between local pressure jump and the two radii of curvature. A thin boundary layer on both sides of the gas-liquid interface is considered with a surface-velocity jump due to pressure-gradient-driven flow with a large density jump and a pressure jump due to surface tension. A near-ellipsoidal shape is predicted using $We$ as a perturbation parameter. Then, the quasi-steady internal liquid-phase stream function and velocity field are predicted, describing internal circulation and a vortex ring structure with vorticity distributed through an inviscid liquid. The gas-phase flow over the oblate droplet is described using a ring doublet as an image within the droplet. The ring-doublet radius is related to We. Gas potential flow results are presented and compared using both the exact analytical solution and a perturbation analysis based on the square root of We. The perturbation analysis provides a lower computational cost. Three analyses for local curvature, liquid circulation, and gas potential flow are matched to yield the velocity and pressure fields. The appropriate radius for the image ring doublet is matched to the square root of We. Liquid-phase stream function, two velocity components in each fluid, and gas potential field are predicted. S Some comments on droplet drag are presented.

physics.flu-dyn↗

arXiv2026

Large-Eddy Simulation and Performance Analysis of a Continuous-Turbine-Burner Stage

This paper reports the first large-eddy simulation of chemically reacting flow in a turbine stage to analyze the influence of fuel injection and combustion on its aerodynamic and thermodynamic performance. Two reacting cases---with four and sixteen fuel injectors at the inlet for each stator passage---are computed and compared against two nonreacting cases, one with four fuel injectors and the other without. The analyses indicate viability for the continuous-turbine-burner (CTB) concept, which offers the potential of significant increase of specific power/thrust of a gas-turbine engine without loss of efficiency. Fuel injection and combustion have minimal influence on the total-pressure loss. Compared with the baseline nonreacting case, the stage work per unit mass increases by 8.5% and 11.5% in the two reacting cases, while the residual work rises by 17.3% and 16.0%, respectively. The two reacting cases exhibit a 14.5% increase of overall work and a thermal efficiency of 44% for the fuel injection. Local high temperature on the rotor blade is suppressed by using a more uniform spanwise distribution of fuel injectors. The work extraction process of a CTB is analyzed from both thermodynamic and mechanical views.

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arXiv2026

Strain-Rate-Consistent $\varepsilon$-Based Non-Premixed Flamelet Model

This numerical study examines a strain-rate inconsistency in the conventional flamelet/progress-variable (FPV) formulation for non-premixed combustion and proposes an alternative coupling based on the turbulence kinetic energy dissipation rate, $\varepsilon$. Two-dimensional Reynolds-averaged Navier-Stokes (RANS) simulations of a transonic accelerating reacting mixing layer are performed using one-step kinetics, a conventional FPV model, and the proposed $\varepsilon$-$Z$ flamelet model. The analysis focuses on the relation between the RANS-computed mean strain-rate field and the local strain rate imposed on the flamelet through the coupling between the flow computation and the flamelet library. In the FPV formulation, the flamelet state is selected through a transported progress variable, whose evolution is governed by advection, diffusion, and chemical production rather than by the local strain-rate environment. The present results show that this can lead to preferential sampling of near-equilibrium flamelet states in high-strain regions, thereby weakening the intended connection between the computed flow field and the strain-rate-controlled flamelet response. In the $\varepsilon$-$Z$ formulation, $\varepsilon$ is used to infer the imposed flamelet strain rate, $S^*$, so that the local flamelet state is directly constrained by the modeled turbulence field and the pressure-dependent flammability limit. Selected species are transported explicitly, allowing products to persist through locally quenched regions, while a reactant-availability scaling limits tabulated source terms when the transported composition departs from the flamelet manifold.

physics.flu-dyn↗

arXiv2025

Flamelet Model with Epsilon Tracking in a Turbine Stator

Combustion within a two-dimensional turbine stator passage is numerically investigated in the context of the turbine-burner concept using a Reynolds-Averaged Navier-Stokes framework coupled with a novel flamelet model. The formulation links resolved-scale turbulence quantities with subgrid flamelet dynamics through the local turbulent kinetic energy dissipation rate, $ε$, which determines the flamelet inflow strain rate. For the first time, combustion of JP-5 is considered in a turbine stator passage as a practical fuel. This is achieved by solving transport equations for 14 major species on the resolved scale, while chemical source terms are obtained from precomputed flamelet libraries based on the HyChem A3 mechanism comprising 119 species and 841 elementary reactions. Model performance is assessed against methane combustion using both a one-step kinetics model and an $ε$-based flamelet formulation employing a 13-species skeletal mechanism. The $ε$-based formulation predicts lower peak flame temperatures due to dissociation effects and approximately 50\% lower net chemical energy addition per unit mass compared with the one-step model, as a result of flame stand-off and downstream strain-rate-induced quenching. For JP-5, the simulations capture combined endothermic pyrolysis and exothermic oxidation processes, leading to vertically displaced reaction zones, increased near-wall temperatures, and larger resolved-scale reaction regions due to the higher flamelet flammability limit relative to methane.

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arXiv2025

Performance of Flamelet Models with Epsilon Tracking for Diffusion Flame Simulations

This work examines the physical consistency of the conventional Flamelet Progress Variable (FPV) model for diffusion flame simulations and and introduces a new compressible flamelet formulation that employs the turbulent kinetic energy dissipation rate, $ε$, as the tracking variable. Two-dimensional Reynolds-averaged Navier-Stokes (RANS) simulations are conducted for a reacting, transonic, turbulent mixing layer to assess the coupling between resolved-scale and subgrid flamelet quantities, with emphasis on the role of strain rate. The FPV model is found to decouple resolved-scale and subgrid strain rates, leading to the preferential selection of equilibrium flamelet solutions in regions of high strain and resulting in nonphysical predictions of heat release and species composition. The proposed $ε$-based formulation restores physical consistency by relating the subgrid flamelet strain rate to $ε$, allowing the flamelet to respond to the local resolved-scale strain field. The inclusion of resolved-scale species transport enables advective and diffusive redistribution of products across locally quenched regions. The results indicate that $ε$ offers a physically consistent tracking variable that connects the sub-grid flamelet model to resolved-scale RANS computations.

physics.flu-dyn↗

arXiv2025

Flamelet Connection to Turbulence Kinetic Energy Dissipation Rate

The turbulence kinetic energy dissipation rate $ε$, from a turbulent combustion computation using either Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES), is proposed for closure with a sub-grid non-premixed flamelet model. The intentions are to avoid the creation of artificial tracking or progress variables and to relate accurately the physics of turbulent non-premixed combustion at the resolved length scales to the small-scale physics where the mixing and chemical reactions occur. The analysis addresses the relations between $ε$ and the strain rate, vorticity, viscous dissipation rate, scalar gradients, scalar dissipation rate, and burning rate at the smallest turbulence length scales where diffusion-controlled burning is faster than at larger length scales and thereby dominant. The imposed strain rate and vorticity on these smallest eddies are determined from the kinetic energy dissipation rate. Thus, an $ε$ value at a specific time and location determines the two mechanical constraints (vorticity and strain rate) on the inflow to the counterflow flamelet. $ε$ affects the sign of the Laplacian of pressure, which must be negative to allow the existence of the counterflow. Using different flamelet models, with and without vorticity, different results for maximum flamelet temperature, integrated flamelet burning rate, and maximum flamelet scalar dissipation rate are obtained. Flamelet models that consider the centrifugal effect of vorticity produce substantial enhancements in the accuracy and completeness of information for a turbulent combustion computation. $ε$ may be used as a tracking variable that connects the sub-grid flamelet model to resolved-scale RANS or LES computations.

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arXiv2024

Three-dimensional Vorticity Effects on Extinction Behavior of Laminar Flamelets

A recent rotational flamelet model is developed and tested with an improved framework of detailed chemistry and transport. The rotational flamelet model incorporates the effects of shear strain and vorticity on local flame behavior and is three-dimensional by nature. A similarity solution reduces the three-dimensional governing equations to ODEs involving a transformation to a non-Newtonian reference frame. A 9-species chemical kinetics model is used for H2-O2 combustion with non-reacting N2. Multiple flamelet cases including non-premixed, premixed, and partially-premixed flames are performed. Across all cases, vorticity extends flammability limits by up to 30% in terms of the ambient extinction strain rate and modifies both local flame structure and mixture composition. For non-premixed flames, where the location of minimum density coincides with the location of peak temperature, the centrifugal force induced by vorticity reduces the mass flow rate through the flame, effectively lowering the local strain rate. This increases residence time, thus extending flammability limits and reducing burning rates. This analysis is done also for premixed and partially-premixed flames. If minimum density lies between the flame zone and the fuel inlet boundary, centrifugal forces do not significantly modify flame behavior. Stable and unstable branches of S-curves for non-premixed and partially-premixed flames and stable branches for premixed flames show extended flammability limits due to vorticity. The capabilities of the rotational flamelet model reveal that vital physics are currently missing from two-dimensional, irrotational, constant-density, flamelet models. Improvements of detailed chemical kinetics, transport formulation, and thermo-physical properties bring the new flamelet model to par in these areas with existing models, while adding new features in terms of physical emulation.

physics.flu-dyn↗

arXiv2024

Vortex Stretching of Non-premixed, Diluted Hydrogen/Oxygen Flamelets

A three-dimensional flamelet model considering vortex stretching with unitary Lewis number is used to simulate diluted hydrogen-oxygen diffusion flames. Non-reacting nitrogen is used as the diluent gas in the fuel stream. Unitary Lewis number provides a common thermal and mass diffusivity from which to create scalar dissipation rate. Both stable and unstable branches of flammability curves (S-curves) are calculated with three vorticity levels and plotted against multiple input and output parameters. The description of the three-dimensional flamelet structure, allowing vorticity and variable density to produce a centrifugal effect, is seen to be necessary for an accurate determination of the $\mathrm{H_2O}$ production rate when ambient inflow strain rate $(S^*)$ and vorticity $(ω)$ are chosen as the key parameters. Maximum temperature and integrated $\mathrm{H_2O}$ production rate each nearly collapse to a single curve when plotted versus maximum scalar dissipation rate $(χ_{max})$ but do not collapse when plotted versus the local maximum strain rate $(S^*_{local})$ or $S^*$. Additionally, $S^*_{local}$ and scalar dissipation rate $(χ)$ depend strongly on vorticity and ambient inflow strain rate. It is argued that the controlling inputs for a flamelet embedded in a turbulent eddy are the ambient vorticity and strain rate which are thus the natural choice of parameterizing variables. These ambient quantities can be readily linked to the averaged or filtered turbulent flow by leveraging cascade theory, as opposed to local strain rate or scalar dissipation rate within the flame zone, which do not have a widely accepted, first-principles scaling connection to the turbulence cascade.

physics.flu-dyn↗

arXiv2024

Turbulent Accelerating Combusting Flows with a Methane-Vitiated Air Flamelet Model

This work presents a numerical study of a diffusion flame in a reacting, two-dimensional, turbulent, viscous, multi-component, compressible mixing layer subject to a large favorable streamwise pressure gradient. The boundary-layer equations are solved coupled with both the $k$-$ω$ and SST turbulence models. A compressible extension of the flamelet progress variable method has been proposed and tested for use with large eddy simulations or Reynolds-averaged Navier-Stokes analyses of the burning of methane in pure air and vitiated air; the latter being particularly relevant in turbine burner scenarios. Effects of the level of detail of the reaction mechanism on the sub-grid and resolved-scale computations are studied. A comparison is made with results obtained using a simplified one-step reaction. The numerical results employing the flamelet model with the more detailed reaction mechanism show faster chemistry, significantly reduced peak temperatures and stronger sensitivity to pressure. Vitiated air flames are found to be dominated by unstable solutions, resulting in a weak flame with substantially lower peak temperature and impeded development, struggling to persist without quenching.

physics.flu-dyn↗

arXiv2024

Unsteady Three-dimensional Rotational Flamelet

A new unsteady flamelet model is developed to be used for sub-grid modeling and coupling with the resolved flow description for turbulent combustion. Difficulties with prior unsteady flamelet models are identified. The model extends the quasi-steady rotational flamelet model which differs from prior models in several critical ways. (i) The effects of shear strain and vorticity are determined, in addition to normal-strain-rate impacts. (ii) The strain rates and vorticity are determined from the conditions of the environment surrounding the flamelet without a contrived progress variable. (iii) The flamelet model is physically three-dimensional but reduced to a one-dimensional, unsteady formulation using similarity. (iv) Variable density is fully addressed in the flamelet model. (v) Non-premixed flames, premixed flames, or multi-branched flame structures are determined rather than prescribed. For both quasi-steady and unsteady cases, vorticity creates a centrifugal force on the flamelet counterflow that modifies the transport rates and burning rate. In the unsteady scenario, new unsteady boundary conditions must be formulated to be consistent with the unsteady equations for the rotating counterflow. Eight boundary values on inflowing scalar and velocity properties and vorticity will satisfy four specific relations and therefore cannot all be arbitrarily specified. The temporal variation of vorticity is connected to the variation of applied normal strain rate through the conservation principle for angular momentum. Limitations on the model concerning fluctuation of the inter-facial plane are identified and conditions under which inter-facial plane fluctuation is negligible are explained. An example of a rotating flamelet counterflow with oscillatory behavior is examined with linearization of the fluctuating variables.

physics.flu-dyn↗

arXiv2023

Numerical Investigation of Diffusion Flame in Transonic Flow with Large Pressure Gradient

A finite-volume method for the steady, compressible, reacting, turbulent Navier-Stokes equations is developed by using a steady-state preserving splitting scheme for the stiff source terms in chemical reaction. Laminar and turbulent reacting flows in a mixing layer with large streamwise pressure gradient are studied and compared to boundary-layer solutions. It reveals that chemical reaction strongly enhances turbulent transport due to intensive production of turbulence by the increased velocity gradients and thus produces large turbulent viscosity in the reaction region. Influence of vitiated air on the combustion process and aerodynamic performance is also investigated for the cases of turbulent mixing layer and highly-loaded transonic turbine cascade. Both cases indicate viability for the turbine-burner concept.

physics.flu-dyn↗

arXiv2023

Combustion Dynamics of Ten-injector Rocket Engine Using Flamelet Progress Variable

The combustion instability is investigated computationally for a ten-injector rocket engine using the compressible flamelet progress variable (FPV) model and detached eddy simulation (DES). An C++ code is developed based on OpenFOAM 4.1 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. The flames at this high pressure level are found having similar structures as those at much lower pressures. A power law is determined to rescale the reaction rate for the progress variable to address the pressure effect. The combustion is also simulated by the one-step-kinetics (OSK) model for comparison with the FPV model. Premixed and diffusion flames are identified locally for both the FPV and OSK models. Study of combustion instability shows that a combined first longitudinal and first tangential mode of 3200 Hz is dominant for the FPV model while the OSK model favors a pure first tangential mode of 2600 Hz. The coupling among pressure oscillation, unsteady transverse flow and helicity fluctuation is discussed. A preliminary study of the resonance in the injectors, which is driven by the acoustic oscillation in the combustion chamber, is also presented.

physics.flu-dyn↗

arXiv2022

Reacting and Non-reacting, Three-dimensional Shear Layers with Spanwise Stretching

A three-dimensional, steady, laminar shear-layer flow spatially developing under a boundary-layer approximation with mixing, chemical reaction, and imposed normal strain is analyzed. The imposed strain creates a counterflow that stretches the vorticity in the spanwise direction. The equations are reduced to a two-dimensional form for three velocity components. The non-reactive and reactive cases of the two-dimensional form of the governing equations are solved numerically, with consideration of the several of parameter inputs such as Damköhler number, Prandtl number, chemical composition, and free-stream velocity ratios. The analysis of the non-reactive case focuses on the mixing between hotter gaseous oxygen and cooler gaseous propane. The free-stream strain rate κis predicted by ordinary differential equations based upon the imposed spanwise pressure variation. One-step chemical kinetics are used to describe diffusion flames and multi-flame structures. The imposed normal strain rate has a significant effect on the width of downstream mixing layers as well as the burning rate. Asymptotically in the downstream direction, a constant width of the shear layer is obtained if imposed normal strain rate is constant. A similar solution with layer width growing with the square root of downstream distance is found when imposed strain rate decreases as the reciprocal of downstream distance.

physics.flu-dyn↗

arXiv2022

Temporal atomization of a transcritical liquid n-decane jet into oxygen

The injection of liquid fuel at supercritical pressures is a relevant but overlooked topic in combustion. Typically, the role of two-phase dynamics is neglected under the assumption that the liquid rapidly transitions to a supercritical state. However, a transcritical domain exists where a sharp phase interface remains. This scenario is the common case in the early times of liquid fuel injection under real-engine conditions involving hydrocarbon fuels. Under such conditions, the dissolution of the oxidizer species into the liquid phase is accelerated due to local thermodynamic phase equilibrium (LTE) and vaporization or condensation can occur at multiple locations along the interface at the same time. Fluid properties vary under species and thermal mixing, with similar liquid and gas mixtures near the interface. As a result of the combination of low, varying surface-tension force and gas-like liquid viscosities, small surface instabilities develop early. The mixing process, interface thermodynamics, and early deformation of a cool liquid n-decane jet surrounded by a hotter moving gas initially composed of pure oxygen are analyzed at various ambient pressures and gas velocities. A two-phase, low-Mach-number flow solver for variable-density fluids is used. The interface is captured using a split Volume-of-Fluid method, generalized for a non-divergence-free liquid velocity and mass exchange across the interface. The importance of transcritical mixing effects over time for increasing pressures is shown. Initially, local deformation features differ considerably from previous incompressible works. Then, the minimal surface-tension force is responsible for the generation of overlapping liquid layers in favor of the classical atomization into droplets. Thus, surface-area growth at transcritical conditions is mainly a consequence of gas-like deformations under shear rather than spray formation.

physics.flu-dyn↗

arXiv2022

A Volume-of-Fluid method for variable-density, two-phase flows at supercritical pressure

A two-phase, low-Mach-number flow solver is created and verified for variable-density liquid and gas with phase change. The interface is sharply captured using a split Volume-of-Fluid method generalized for a non-divergence-free liquid velocity and with mass exchange across the interface. Mass conservation to machine-error precision is achieved in the limit of incompressible liquid. This model is implemented for two-phase mixtures at supercritical pressure but subcritical temperature conditions for the liquid, as it is common in the early times of liquid hydrocarbon injection under real-engine conditions. The dissolution of the gas species into the liquid phase is enhanced, and vaporization or condensation can occur simultaneously at different interface locations. Greater numerical challenges appear compared to incompressible two-phase solvers that are successfully addressed for the first time: (a) local thermodynamic phase equilibrium (LTE) and jump conditions determine the interface solution (e.g., temperature, composition, surface-tension coefficient); (b) a real-fluid thermodynamic model is considered; and (c) phase-wise values for certain variables (e.g., velocity) are obtained via extrapolation techniques. The increased numerical cost is alleviated with a split pressure-gradient technique to solve the pressure Poisson equation (PPE) for the low-Mach-number flow. Thus, a Fast Fourier Transform (FFT) method is implemented, directly solving the continuity constraint without an iterative process. Various verification tests show the accuracy and viability of the current 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 is analyzed. Other features of supercritical liquid injection are also shown.

physics.flu-dyn↗

arXiv2022

Inward Swirling Flamelet Model

A new rotational flamelet model with inward swirling flow through a stretched vortex tube is developed for sub-grid modeling to be coupled with the resolved flow for turbulent combustion. The model has critical new features compared to existing models. (i) Non-premixed flames, premixed flames, or multi-branched flame structures are determined rather than prescribed. (ii) The effects of vorticity and the related centifugal acceleration are determined. (iii) The strain rates and vorticity applied at the sub-grid level can be 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. (vi) The inward swirl is created by vorticity combined with two compressive normal strain components; this feature distinguishes the model from counterflow flamelet models. 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, burning rates, and flammability limits. Sample computations of the inward swirling rotational flamelet model without coupling to the resolved flow are presented to demonstrate the importance of the new features. Premixed, nonpremixed, and multi-branched flame structures are examined. Parameter surveys are made with rate of normal strain, vorticity, Damköhler number, and Prandtl number. The centrifugal effect has interesting consequences when combined with the variable-density field. Flow direction can reverse; burning rates can be modified; flammability limits can be extended.

physics.flu-dyn↗

arXiv2022

Physics-Aware Neural Network Flame Closure for Combustion Instability Modeling in a Single-Injector Engine

Neural networks (NN) are implemented as sub-grid flame models in a large-eddy simulation of a single-injector liquid-propellant rocket engine with the aim to replace a look-up table approach. The NN training process presents an extraordinary challenge. The multi-dimensional combustion instability problem involves multi-scale lengths and characteristic times in an unsteady flow problem with nonlinear acoustics, addressing both transient and dynamic-equilibrium behaviors, superimposed on a turbulent reacting flow with very narrow, moving flame regions. Accurate interpolation between the points of the training data becomes vital. A major novel aspect of the proposed NNs is that they are trained to reproduce relevant portions of the information stored in a flamelet table by using only limited data from a few CFD simulations of a single-injector liquid-propellant rocket engine under different dynamical configurations. This is made possible by enriching the training set with contrived data resulting from the physical characteristics of the combustion model and also by including the flame temperature as an extra input to the NNs that are trained to model other flame variables of interest. These physics-aware NN-based closure models are first tested offline by comparing them directly with the flamelet table and then are successfully implemented into CFD simulations in place of the flamelet table and verified on various dynamical configurations. The results from those tests compare favorably with counterpart table-based CFD simulations. Computational advantages of the approach are discussed.

physics.flu-dyn↗

arXiv2021

Liquid-jet instability at high pressures with real-fluid interface thermodynamics

The injection of liquid fuel at supercritical pressures is a relevant topic in combustion, but usually overlooked. In the past, the wrong assumption whereby the liquid experiments a fast transition to a supercritical state was made, thus neglecting any role of two-phase interface dynamics in the early stages of the atomization process. However, recent studies have shown that local thermodynamic phase equilibrium and mixing between the involved species allow the coexistence of both phases in this pressure range. In this work, a Volume-of-Fluid method adapted to variable-density real fluids is used to solve the low-Mach-number governing equations coupled with a thermodynamic model based on the Soave-Redlich-Kwong equation of state. The mixing process, interface thermodynamics and early deformation of a cool liquid jet composed of n-decane surrounded by a hotter gas composed of oxygen at 150 bar are analyzed. Although heat conducts from the hotter gas into the liquid, net condensation can provide the proper local energy balance at high pressures. Then, vaporization and condensation may happen simultaneously at different interface locations. As pressure increases, liquid and gas mixtures become more alike in the vicinity of the interface. Thus, a combination of low surface tension force and gas-like liquid viscosities causes an early growth of surface instabilities. Early results indicate some similarity with high-Weber-number incompressible flows. The role of vortex dynamics on the interface deformation is analyzed by using the dynamical vortex identification method.

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