Entropy production and the g-scheme

Spatially homogeneous batch reactor systems are characterized by the simultaneous presence of a wide range of time scales. When the dynamics of such reactive systems develop very-slow and very-fast time scales separated by a range of active time scales, with large gaps in the fast/active and slow/active time scales, then it is possible to achieve multi-scale adaptive model reduction along-with the integration of the governing ordinary differential equations using the G-Scheme framework. The G- Scheme assumes that the dynamics is decomposed into active, slow, fast, and when applicable, invariant subspaces. We computed the contribution to entropy production by the four subspaces, with reference to a constant volume, adiabatic reactor. The numerical experiments indicate that the contributions of the fast and slow subspaces are much smaller than that of the active subspace

Entropy production at all scales

Spatially homogeneous systems are characterized by the simultaneous presence of a wide range of time scales. When the dynamics of such reactive systems develop very-slow and very-fast time scales separated by a range of active time scales, with large gaps in the fast/active and slow/active time scales, then it is possible to achieve multi-scale adaptive model reduction along-with the integration of the governing ordinary differential equations using the G-Scheme framework. The G-Scheme assumes that the dynamics is decomposed into active, slow, fast, and when applicable, invariant subspaces. We derive the expressions that express the direct link between time scales and entropy production by resorting to the estimates provided by the G-Scheme. With reference to a constant volume, adiabatic batch reactor, we compute the contribution to entropy production by the four subspaces. The numerical experiments show that, as indicated by the theoretical derivation, the contribution to entropy production of the fast subspace is of the same magnitude of the error threshold chosen for the numerical integration, and that the contribution of the slow subspace is generally much smaller than that of the active subspace

Dynamical system analysis of ignition phenomena using the tangential stretching rate concept

We analyze ignition phenomena by resorting to the stretching rate concept formerly introduced in the study of dynamical systems. We construct a Tangential Stretching Rate (TSR) parameter by combining the concepts of stretching rate with the decomposition of the local tangent space in eigen-modes. The main feature of the TSR is its ability to identify unambiguously the most energetic scale at a given space location and time instant. The TSR depends only on the local composition of the mixture, its temperature and pressure. As such, it can be readily computed during the post processing of computed reactive flow fields, both for spatially homogeneous and in-homogenous systems. Because of the additive nature of the TSR, we defined a normalized participation index measuring the relative contribution of each mode to the TSR. This participation index to the TSR can be combined with the mode amplitude participation Index of a reaction to a mode – as defined in the Computational Singular Perturbation (CSP) method – to obtain a direct link between a reaction and TSR. The reactions having both a large participation index to the TSR and a large CSP mode amplitude participation index are those contributing the most to both the explosive and relaxation regimes of a reactive system. This information can be used for both diagnostics and for the simplification of kinetic mechanisms. We verified the properties of the TSR with reference to three nonlinear planar models (one for isothermal branched-chain reactions, one for a non-isothermal, one-step system, and for non-isothermal branched-chain reactions), to one planar linear model (to discuss issues associated with non-normality), and to test problems involving hydro-carbon oxidation kinetics. We demonstrated that the reciprocal of the TSR parameter is the proper characteristic chemical time scale in problems involving multi-step chemical kinetic mechanisms, because (i) it is the most relevant time scale during both the explosive and relaxation regimes and (ii) it is intrinsic to the kinetics, that is, it can be identified without the need of any ad hoc assumption

Numerical investigation of unsteady laminar methane/LOx flamelet at supercritical pressures

High-pressure combustion devices, such as liquid rocket engines, are usually characterized by transcritical and supercritical operating conditions. Propellants injected in the combustion chamber experience extremely high den- sity gradients and real fluid effects. In the present study, real fluid effects on flame structure are investigated in the framework of unsteady laminar flamelet equations, a well established representation and diagnostic tool for non pre- mixed combustion transient phenomena. Real fluid thermodynamic properties are taken into account by means of a computationally efficient cubic equation of state written in a general and comprehensive three-parameter fashion. High-pressure conditions for unsteady flame structure calculations and analysis are chosen as a representative range of a methane/liquid-oxygen rocket engine operating conditions. Particular focus is posed on the constant pressure specific heat behavior at low temperature, which influences the time evolution of the flame structure. Moreover time accurate integration of flamelet equations represent the very first building block of a conditional moment closure for supercritical turbulent combustion

Evaporation and clustering of ammonia droplets in a hot environment

Recent developments in the transition to zero-carbon fuels show that ammonia is a valid candidate for combustion. However, liquid ammonia combustion is difficult to stabilize due to a large latent heat of evaporation, which generates a strong cooling effect that adversely affects the flame stabilization and combustion efficiency. In addition, the slow burning rate of ammonia enhances the undesired production of NOx and N2O. To increase the flame speed, ammonia must be blended with a gaseous fuel having a high burning rate. In this context, a deeper understanding of the droplet dynamics is required to optimize the combustor design. To provide reliable physical insights into diluted ammonia sprays blended with gaseous methane, direct numerical simulations are employed. Three numerical experiments were performed with cold, standard, and hot ambient in nonreactive conditions. The droplet radius and velocity distribution, as well as the mass and heat coupling source terms are compared to study the effects on the evaporation. Since the cooling effect is stronger than the heat convection between the droplet and the environment in each case, ammonia droplets do not experience boiling. On the other hand, the entrainment of dry air into the ammonia-methane mixture moves the saturation level beyond 100% and droplets condense. The aforementioned phenomena are found to strongly affect the droplet evolution. Finally, a three-dimensional Voronoi analysis is performed to characterize the dispersive or clustering behavior of droplets by means of the definition of a clustering index

A joint numerical study of multi-regime turbulent combustion

This article presents a joint numerical study on the Multi Regime Burner configuration. The burner design consists of three concentric inlet streams, which can be operated independently with different equivalence ratios, allowing the operation of stratified flames characterized by different combustion regimes, including premixed, non-premixed, and multi-regime flame zones. Simulations were performed on three LES solvers based on different numerical methods. Combustion kinetics were simplified by using tabulated or reduced chemistry methods. Finally, different turbulent combustion modeling strategies were employed, covering geometrical, statistical, and reactor based approaches. Due to this significant scattering of simulation parameters, a conclusion on specific combustion model performance is impossible. However, with ten numerical groups involved in the numerical simulations, a rough statistical analysis is conducted: the average and the standard deviation of the numerical simulation are computed and compared against experiments. This joint numerical study is therefore a partial illustration of the community's ability to model turbulent combustion. This exercise gives the average performance of current simulations and identifies physical phenomena not well captured today by most modeling strategies. Detailed comparisons between experimental and numerical data along radial profiles taken at different axial positions showed that the temperature field is fairly well captured up to 60 mm from the burner exit. The comparison reveals, however, significant discrepancies regarding CO mass fraction prediction. Three causes may explain this phenomenon. The first reason is the higher sensitivity of carbon monoxide to the simplification of detailed chemistry, especially when multiple combustion regimes are encountered. The second is the bias introduced by artificial thickening, which overestimates the species’ mass production rate. This behavior has been illustrated by manufacturing mean thickened turbulent flame brush from a random displacement of 1-D laminar flame solutions. The last one is the influence of the subgrid-scale flame wrinkling on the filtered chemical flame structure, which may be challenging to model.</p

A joint numerical study of multi-regime turbulent combustion

This article presents a joint numerical study on the Multi Regime Burner configuration. The burner design consists of three concentric inlet streams, which can be operated independently with different equivalence ratios, allowing the operation of stratified flames characterized by different combustion regimes, including premixed, non-premixed, and multi-regime flame zones. Simulations were performed on three LES solvers based on different numerical methods. Combustion kinetics were simplified by using tabulated or reduced chemistry methods. Finally, different turbulent combustion modeling strategies were employed, covering geometrical, statistical, and reactor based approaches. Due to this significant scattering of simulation parameters, a conclusion on specific combustion model performance is impossible. However, with ten numerical groups involved in the numerical simulations, a rough statistical analysis is conducted: the average and the standard deviation of the numerical simulation are computed and compared against experiments. This joint numerical study is therefore a partial illustration of the community's ability to model turbulent combustion. This exercise gives the average performance of current simulations and identifies physical phenomena not well captured today by most modeling strategies. Detailed comparisons between experimental and numerical data along radial profiles taken at different axial positions showed that the temperature field is fairly well captured up to 60 mm from the burner exit. The comparison reveals, however, significant discrepancies regarding CO mass fraction prediction. Three causes may explain this phenomenon. The first reason is the higher sensitivity of carbon monoxide to the simplification of detailed chemistry, especially when multiple combustion regimes are encountered. The second is the bias introduced by artificial thickening, which overestimates the species’ mass production rate. This behavior has been illustrated by manufacturing mean thickened turbulent flame brush from a random displacement of 1-D laminar flame solutions. The last one is the influence of the subgrid-scale flame wrinkling on the filtered chemical flame structure, which may be challenging to model.</p

Optimal Shape Design of Supersonic, Mixed-Compression, Fixed-Geometry Air Intakes for SSTO Mission Profiles

The problem of maximizing the performance of a fixed-geometry air intake geometry of a vehicle accelerating over a wide range of flight Mach number is addressed. An extension of the Seddon-Goldsmlth procedure is used to estimate the flow pattern involving a curved bowshock, a triple point interaction, and wall shock reflection, which characterizes the subcritical regime of operations. The approximate model has been validated against detailed CFD calculations of the flowfield about the air intake. The approximate model is adopted to find the geometry that optimizes the fuel-to-mass ratio over a constant dynamic pressure trajectory