Direct numerical simulation of a hypersonic transitional boundary layer at suborbital enthalpies

A Mach-10 hypersonic boundary layer of air overriding a cold, isothermal, non-catalytic flat wall, and with a stagnation enthalpy of 21.6 MJ kg−1, is analysed using direct numerical simulations. The calculations include multicomponent transport, equilibrium vibrational excitation and chemical kinetics for air dissociation. The initially laminar boundary layer undergoes transition to turbulence by the resonance of a two-dimensional mode injected by a suction-and-blowing boundary condition imposed over a narrow spanwise porous strip. The ensuing turbulent boundary layer has a momentum Reynolds number of 3826 near the outflow of the computational domain. The relatively low temperature of the free stream renders the air chemically frozen there. However, the high temperatures generated within the boundary layer by viscous aerodynamic heating, peaking at a wall-normal distance y⋆≃10--20 in semi-local viscous units, lead to air dissociation in under-equilibrium amounts equivalent to 4 %–7 % on a molar basis of atomic oxygen, along with smaller concentrations of nitric oxide, which is mainly produced by the Zel'dovich mechanism, and of atomic nitrogen, the latter being mostly in steady state. A statistical analysis of the results is provided, including the streamwise evolution of (a) the skin friction coefficient and dimensionless wall heat flux; (b) the mean profiles of temperature, velocity, density, molar fractions, chemical production rates and chemical heat-release rate; (c) the Reynolds stresses and root-mean-squares of the fluctuations of temperature, density, pressure, molar fractions and chemical heat-release rate; and (d) the temperature/velocity and mass-fraction/velocity correlations

Source terms for calculations of vaporizing and burning fuel sprays with non-unity Lewis numbers in gases with temperature-dependent thermal conductivities

Liquid-fueled burners are used in a number of propulsion devices ranging from internal combustion engines to gas turbines. The structure of spray flames is quite complex and involves a wide range of time and spatial scales in both premixed and non-premixed modes (Williams 1965; Luo et al. 2011). A number of spray-combustion regimes can be observed experimentally in canonical scenarios of practical relevance such as counterflow diffusion flames (Li 1997), as sketched in figure 1, and for which different microscalemodelling strategies are needed. In this study, source terms for the conservation equations are calculated for heating, vaporizing and burning sprays in the single-droplet combustion regime. The present analysis provides extended formulation for source terms, which include non-unity Lewis numbers and variable thermal conductivities

Flamelet structures in spray ignition

In typical liquid-fueled burners the fuel is injected as a high-velocity liquid jet that breaks up to form the spray. The initial heating and vaporization of the liquid fuel rely on the relatively large temperatures of the sourrounding gas, which may include hot combustion products and preheated air. The heat exchange between the liquid and the gas phases is enhanced by droplet dispersion arising from the turbulent motion. Chemical reaction takes place once molecular mixing between the fuel vapor and the oxidizer has occurred in mixing layers separating the spray flow from the hot air stream. Since in most applications the injection velocities are much larger than the premixed-flame propagation velocity, combustion stabilization relies on autoignition of the fuel-oxygen mixture, with the combustion stand-off distance being controlled by the interaction of turbulent transport, droplet heating and vaporization, and gas-phase chemical reactions. In this study, conditions are identified under which analyses of laminar flamelets canshed light on aspects of turbulent spray ignition. This study extends earlier fundamental work by Liñan & Crespo (1976) on ignition in gaseous mixing layers to ignition of sprays. Studies of laminar mixing layers have been found to be instrumental in developing un-derstanding of turbulent combustion (Peters 2000), including the ignition of turbulent gaseous diffusion flames (Mastorakos 2009). For the spray problem at hand, the configuration selected, shown in Figure 1, involves a coflow mixing layer formed between a stream of hot air moving at velocity UA and a monodisperse spray moving at velocity USUA. The boundary-layer approximation will be used below to describe the resulting sl ender flow, which exhibits different igniting behaviors depending on the characteristics of t he fuel. In this approximation, consideration of the case U A = U S enables laminar ignition distances to be related to ignition times of unstrained spray flamelets, thereby pro viding quantitative information of direct applicability in regions of low scala r dissipation-rate in turbulent reactive flows (see the discussion in pp. 181–186 of Peters (2000)) . This report is organized as follows. Effects of droplet dispersion dynamics on ignition of sprays in turbulent mixing layers are discussed in Section 2. The formulation f or ignition in laminar mixing layers is outlined in Sections 3 and 4. The results are presented in Section 5. In Section 6, the mixture-fraction field and associated scalar dissipat ion rates for spray ignition are discussed. Finally, some brief conclusions are drawn in Section 7

The role of separation of scales in the description of spray combustion

The present paper deals with the description of the interacting multiscale processes governing spray vaporization and combustion downstream from the near-injector atomization region in liquid-fueled burners. One of the main objectives is to emphasize the progress made in the mathematical description and understanding of reactive spray flows by incorporation of rationally derived simplifications based on the disparity of length and time scales present in the problem. In particular, we aim to show how the disparity of the scales that correspond – with increasing values of their orders of magnitude – to the droplet size, interdroplet spacing, and width of the spray jets, ensures the validity of their homogenized description. The two-way coupling associated with exchanges of mass, momentum, and energy between the gas and the liquid phases is dominated by the homogenized exchanges with the gas provided collectively by the droplets, and not by the direct interaction between neighboring droplets. The formulation is used as a basis to address nonpremixed spray diffusion flames in the Burke-Schumann limit of infinitely fast chemical reactions, with the conservation equations written in terms of chemistry-free coupling functions that allow for general nonunity Lewis numbers of the fuel vapor. Laminar canonical problems that have been used in the past to shed light on different aspects of spray-combustion phenomena are also discussed, including spherical spray clouds and structures of counterflow spray flames in mixing layers. The presentation ends with a brief account of some open problems and modeling challenges

Regimes of spray vaporization and combustion in counterflow configurations

This article addresses the problem of spray vaporization and combustion in axisymmetric opposed-jet configurations involving a stream of hot air counterflowing against a stream of nitrogen carrying a spray of fuel droplets. The Reynolds numbers of the jets are assumed to be large, so that mixing of the two streams is restricted to a thin mixing layer that separates the counterflowing streams. The evolution of the droplets in their feed stream from the injection location is seen to depend fundamentally on the value of the droplet Stokes number, St, defined as the ratio of the droplet acceleration time to the mixing layer strain time close to the stagnation point. Two different regimes of spray vaporization and combustion can be identified depending on the value of St. For values of St below a critical value, equal to 1/4 for dilute sprays with small values of the spray liquid mass loading ratio, the droplets decelerate to approach the gas stagnation plane with a vanishing axial velocity. In this case, the droplets located initially near the axis reach the mixing layer, where they can vaporize due to the heat received from the hot air, producing fuel vapor that can burn with the oxygen in a diffusion flame located on the air side of the mixing layer. The character of the spray combustion is different for values of St of order unity, because the droplets cross the stagnation plane and move into the opposing air stream, reaching distances that are much larger than the mixing layer thickness before they turn around. The vaporization of these crossing droplets, and also the combustion of the fuel vapor generated by them, occur in the hot air stream, without significant effects of molecular diffusion, generating a vaporization-assisted nonpremixed flame that stands on the air side outside the mixing layer. Separate formulations will be given below for these two regimes of combustion, with attention restricted to the near-stagnation-point region, where the solution is self-similar and all variables are only dependent on the distance to the stagnation plane. The resulting formulations display a reduced number of controlling parameters that effectively embody dependences of the structure of the spray flame on spray dilution, droplet inertia, and fuel preferential diffusion. Sample solutions are given for the limiting cases of pure vaporization and of infinitely fast chemistry, with the latter limit formulated in terms of chemistry-free coupling functions that allow for general nonunity Lewis numbers of the fuel vapor

Dynamics of thermal ignition of spray flames in mixing layers

Conditions are identified under which analyses of laminar mixing layers can shed light on aspects of turbulent spray combustion. With this in mind, laminar spray-combustion models are formulated for both non-premixed and partially premixed systems. The laminar mixing layer separating a hot-air stream from a monodisperse spray carried by either an inert gas or air is investigated numerically and analytically in an effort to increase understanding of the ignition process leading to stabilization of high-speed spray combustion. The problem is formulated in an Eulerian framework, with the conservation equations written in the boundary-layer approximation and with a one-step Arrhenius model adopted for the chemistry description. The numerical integrations unveil two different types of ignition behaviour depending on the fuel availability in the reaction kernel, which in turn depends on the rates of droplet vaporization and fuel-vapour diffusion. When sufficient fuel is available near the hot boundary, as occurs when the thermochemical properties of heptane are employed for the fuel in the integrations, combustion is established through a precipitous temperature increase at a well-defined thermal-runaway location, a phenomenon that is amenable to a theoretical analysis based on activation-energy asymptotics, presented here, following earlier ideas developed in describing unsteady gaseous ignition in mixing layers. By way of contrast, when the amount of fuel vapour reaching the hot boundary is small, as is observed in the computations employing the thermochemical properties of methanol, the incipient chemical reaction gives rise to a slowly developing lean deflagration that consumes the available fuel as it propagates across the mixing layer towards the spray. The flame structure that develops downstream from the ignition point depends on the fuel considered and also on the spray carrier gas, with fuel sprays carried by air displaying either a lean deflagration bounding a region of distributed reaction or a distinct double-flame structure with a rich premixed flame on the spray side and a diffusion flame on the air side. Results are calculated for the distributions of mixture fraction and scalar dissipation rate across the mixing layer that reveal complexities that serve to identify differences between spray-flamelet and gaseous-flamelet problems

Direct numerical simulation of a hypersonic transitional boundary layer at suborbital enthalpies

A Mach-10 hypersonic boundary layer of air overriding a cold, isothermal, non-catalytic flat wall, and with a stagnation enthalpy of 21.6 MJ kg(-1), is analysed using direct numerical simulations. The calculations include multicomponent transport, equilibrium vibrational excitation and chemical kinetics for air dissociation. The initially laminar boundary layer undergoes transition to turbulence by the resonance of a two-dimensional mode injected by a suction-and-blowing boundary condition imposed over a narrow spanwise porous strip. The ensuing turbulent boundary layer has a momentum Reynolds number of 3826 near the outflow of the computational domain. The relatively low temperature of the free stream renders the air chemically frozen there. However, the high temperatures generated within the boundary layer by viscous aerodynamic heating, peaking at a wall-normal distance y(star) similar or equal to 10-20 in semi-local viscous units, lead to air dissociation in under-equilibrium amounts equivalent to 4 %-7% on a molar basis of atomic oxygen, along with smaller concentrations of nitric oxide, which is mainly produced by the Zel'dovich mechanism, and of atomic nitrogen, the latter being mostly in steady state. A statistical analysis of the results is provided, including the streamwise evolution of (a) the skin friction coefficient and dimensionless wall heat flux; (b) the mean profiles of temperature, velocity, density, molar fractions, chemical production rates and chemical heat-release rate; (c) the Reynolds stresses and root-mean-squares of the fluctuations of temperature, density, pressure, molar fractions and chemical heat-release rate; and (d) the temperature/velocity and mass-fraction/velocity correlations

Aerodynamic generation of electric fields in turbulence laden with charged inertial particles

Self-induced electricity, including lightning, is often observed in dusty atmospheres. However, the physical mechanisms leading to this phenomenon remain elusive as they are remarkably challenging to determine due to the high complexity of the multi-phase turbulent flows involved. Using a fast multi-pole method in direct numerical simulations of homogeneous turbulence laden with hundreds of millions of inertial particles, here we show that mesoscopic electric fields can be aerodynamically created in bi-disperse suspensions of oppositely charged particles. The generation mechanism is self-regulating and relies on turbulence preferentially concentrating particles of one sign in clouds while dispersing the others more uniformly. The resulting electric field varies over much larger length scales than both the mean inter-particle spacing and the size of the smallest eddies. Scaling analyses suggest that low ambient pressures, such as those prevailing in the atmosphere of Mars, increase the dynamical relevance of this aerodynamic mechanism for electrical breakdown