David Katoshevski

Vaporization Damköhler Number and Enrichment Effects in Spray Diffusion Flames in an Oscillating Flow Field

The sensitivity to the vaporization Damköhler number of the behavior of a coflow laminar spray diffusion flame in an oscillating flow field is investigated. Droplet grouping induced by the host gas flow oscillations is accounted for, and its effect is described through a specially constructed model for the vaporization Damköhler number that responds to the proximity of the droplets as they cluster. A formal analytical solution is developed, and the dynamics of the spray flame front shapes and thermal fields are deduced. Computed results demonstrate how strongly the vaporization Damköhler number impacts on the type of primary homogeneous flame formed and on the possible existence of multiple flame sheets as the flow field oscillates. In addition, isolated regions of high fuel vapor concentrations are produced by fuel droplet enrichment. The presence of resulting parallel fluctuating thermal fields indicates a potential impact on undesirable pollutants production.

Polydisperse spray diffusion flames in oscillating flow

The phenomenon of droplet clustering or grouping found when a spray of droplets is moving in an oscillating host flow field is investigated for the case of a polydisperse spray that fuels a laminar co-flow diffusion flame. A mathematical solution is developed for the liquid phase based on use of small Stokes numbers for size sections into which the polydisperse spray size distribution is divided. Droplet clustering in the oscillatory flow field is accounted for by constructing a special model for the sectional vaporization Damkohler numbers in accordance with droplet size. Combining this with a formal solution for a gas phase Schvab-Zeldovich variable yields the means whereby flame dynamics can be described. Results calculated from this solution demonstrate that preferential droplet size behaviour (with smaller droplets tending to cluster to a greater extent and reduce the vaporization Damkohler number more than larger ones) can have a major impact on the flame dynamics through local droplet enrichment with attendant consequences on the production of fuel vapour. The dynamics of the sort of flame (over- or under-ventilated) and the occurrence of flame pinching leading to multiple flame sheets are altered under these circumstances. However, potential control of the actual initial spray polydispersity may reduce the intensity of such effects.

Particle Number Reduction in Automotive Exhausts Using Acoustic Metamaterials

Air pollution caused by exhaust particulate matter (PM) from vehicular traffic is a major health issue. Increasingly strict regulations of vehicle emission have been introduced and efforts have bee ...

Similarity solutions for the evolution of unsteady spray diffusion flames in vortex flows

ABSTRACT A new mathematical analysis for the dynamics of laminar spray diffusion flames in the vicinity of a vortex flow field is presented. The governing equations for a spray evaporating in an unsteady vortex are studied. New similarity solutions are found for the dynamics of the spray and the flame it supports. Analytical solutions for the spray flames are derived using Shvab-Zeldovich parameters, through which the radial evolution of the flames is found. The results based on the solution reveal the significant effects vorticity and droplet evaporation have on the flame dynamics. An extinction analysis is carried out which maps the influence of the evaporation coefficient and vortex intensity on flame extinguishment. A number of competing factors such as vortex intensity and heat loss due to evaporation were found to be responsible for flame extinction. Despite the model’s simplicity, its predictions offer new insights into the driving mechanisms of more complex spray-combustion situations in which droplets are evaporating in vortical environments.

A new mechanism for size separation of particles immersed in a fluid

Work presented deals with a new mechanism for particle size-separation based on differential grouping induced by a controlled oscillating flow field. This separation by size may be used for coagulation of like-sized particles. Flow oscillations are induced by a pulsating sphere. The dynamics of particles immersed in such a flow field and their trajectories are analysed mathematically based on perturbation analysis. It is shown that in proximity to the sphere, particle trajectories display strong dependence on particle size (through particle Stokes number), far more so than on initial position. Grouping behaviour is observed under specific operating conditions, and this suggests feasibility of applications in filtration systems, as well as for size-based separation.

Polydisperse spray flames in vortex flows

A new mathematical analysis of the dynamics of laminar spray diffusion flames in the vicinity of a vortex flow field is presented. The governing equations for a spray evaporating in an unsteady vortex are studied. New similarity solutions are found for the dynamics of the spray and the flame it supports. Analytical solutions for the spray flames are derived using Schvab-Zeldovich parameters, through which the radial evolution of the flames is found. The results based on the solution reveal the significant influence the droplets size has on the diffusion flame dynamics in the vicinity of vortical flows. Introduction The dynamics of evaporating sprays play an important role in many practical combustion applications such as gasturbines and swirl combustion chambers. The interactions between a gaseous diffusion flame and a vortex flow-field were extensively studied [1, 2, 3]. In a previous study of Dagan et al. [4], unsteady turbulent spray-flame instability in a concentric jet combustion chamber was studied using large eddy simulations (LES). In their study, droplet grouping and ligament structures were identified in the vicinity of vortices in large recirculation zones. Using direct numerical simulations (DNS) of Diesel spray combustion in the vicinity of a recirculation zone, Shinjo et al. [5] showed that when droplets are larger than the Kolmogorov microscale, mixing is strongly enhanced by the presence of droplets and fuel vapor clusters are likely to form quickly when the droplet number density is high. They suggested that external group combustion is likely to occur near the recirculation zone. The effects of droplet clustering on evaporation were thoroughly discussed by Sirignano [6] and Harstad et al. [7]. Clusters of droplets are formed in vortical flows, as they accelerate towards the outer region of the vortex[8]. The dynamics of dropletvortex interactions and their influence on the structure of an evaporating spray was numerically studied by [9]. Droplet-vortex interaction in the Karman-vortex street was studied by Burger et al. [10], using DNS and a theoretical approach imposing a harmonically oscillating flow field. Recently, Franzelli et al. [11] numerically characterized the regimes of spray flame-vortex interactions. They used a two-dimensional Oseen type vortex in their study. However, their study relates to a vortex moving perpendicularly through an opposed flow spray sheet. These studies emphasize the need for a more fundamental understanding of the influence of droplet dynamics on combustion in vortical environments and recirculating flows, which appear in turbulent, as well as laminar environments. The objective of the present work is to analytically study the influence of a vortex flow-field has on the evaporation and combustion of polydisperse sprays. A new mathematical formulation for the dynamics of polydisperse sprays in the vicinity of a vortex flow field is presented. The governing equations for a polydisperse spray evaporating in an unsteady vortex and the diffusion flame they support are studied and new similarity solutions are found for the dynamics of the spray flames, using the sectional approach (following Tambour, Greenberg and Katoshevski [14, 15, 16, 17]). Finally, preliminary results are shown for the influence of polydispersity on the reacting diffusion sprayflames in the vicinity of vortical flows. Governing equations Gas phase The equations for a polydisperse spray evaporating in a two-dimensional unsteady axisymmetric vortex flow are presented. A polar coordinate system (r, θ) is employed in the following derivation of equations. As a result of our assumption of an axisymmetric flow, all derivatives with respect to the angular coordinate θ are assumed zero. A constant density for the host gas is assumed. The constant density assumption is frequently adopted in diffusion flame studies under conditions in which the fuel and the oxidant are heavily diluted so that the heat released by chemical reaction is small in comparison with the thermal energy of the mixture and gas expansion is negligible. Under these assumptions, the governing gas-phase equations are Gas-phase momentum: ∂vr ∂t + vr ∂vr ∂r − v2 θ r = − 1 ρ ∂p ∂r + ν ∂ ∂r ( 1 r ∂ ∂r (rvr) ) − Ns ∑ j=1 Q̃jFr,j − Ṡev,r (1) ∂vθ ∂t + vr ∂vθ ∂r + vrvθ r = ν ∂ ∂r ( 1 r ∂ ∂r (rvθ) ) − Ns ∑ j=1 Q̃jFθ,j − Ṡev,θ (2) This work is licensed under a Creative Commons 4.0 International License (CC BY-NC-ND 4.0). EDITORIAL UNIVERSITAT POLITÈCNICA DE VALÈNCIA ILASS – Europe 2017, 6-8 Sep. 2017, Valencia, Spain where ρ is the gas-phase density, vr is the gas radial velocity, vθ is the tangential velocity of the host gas, ν is the kinematic viscosity and p is the pressure. Q̃j denotes mass fraction of the liquid fuel in size section j and Ns is the total number of sections. Ṡev accounts for the momentum transferred to the host gas by the vapors. Fr,j and Fθ,j describe the interaction between the gas phase and the droplets of size section j in the radial and tangential directions, respectively, being proportional to the relative velocity between the droplets and the gas Fr,j = τ −1 j (vr − ur,j); Fθ,j = τ −1 j (vθ − uθ,j) (3) where ur,j and uθ,j are the radial and tangential velocities of the droplets of section j, respectively. τj is the sectional droplet relaxation time-scale. The conservation equations for the vapour mass fraction of the fuel, mf and the oxidizer, mo, and energy equation are given by ∂mf ∂t + 1 r ∂ ∂r (rvrmf ) = Df 1 r ∂ ∂r (r ∂mf ∂r ) + CQ− 1 ρ S̃R,f (4) ∂mo ∂t + 1 r ∂ ∂r (rvrmo) = Do 1 r ∂ ∂r (r ∂mo ∂r )− 1 ρ S̃R,o (5) ∂T ∂t + 1 r ∂ ∂r (rvrT ) = k ρCp 1 r ∂ ∂r (r ∂T ∂r )− hv Cp CQ+ 1 ρCp S̃R,T (6) following Katoshevski et al. [16]. T is the temperature, k and Cp are the gas conduction coefficient and specific heat at constant pressure, respectively. hv accounts for the latent heat of vaporization, Df and Do are the diffusion coefficients, and we assume all species have the same CP value. The SR terms are the reaction source terms for each equation, based on the assumption of a global reaction of the form Fuel + ζsOxidant → Products, where ζs is the stoichiometric coefficient. However, as will be showed in the following sections, Schvab-Zeldovich type variables will be formulated in the similarity coordinate. Hence, an explicit treatment of the reaction terms will not be required. Liquid spray phase In the present study the equations for the reacting flow and their solutions are obtained only for a mono-sectional case. However, the sectional equations for the dynamics of sprays are presented here in a polydisperse formulation for the sake of generality. The multi-size droplet population is represented by a set of Ns sectional conservation equations of the form ∂Q̃j ∂t + 1 r ∂ ∂r (rur,jQ̃j) = −CjQ̃j +Bj,j+1Q̃j+1; j = 1, 2, ..., Ns (7) where the coefficient Bj,j+l accounts for droplets from section (j + 1) which are added to section j during their evaporation, whereas Cj accounts for evaporation of droplets within section j and for droplets that move from section j to section (j − 1). In reality, the evaporation coefficient is a complicated function of the temperature differential between the droplets and the surrounding gas, the diffusivity and other properties of the fuel and its surroundings. Here the d − law underlies the definition of the evaporation coefficient. Reasonably accurate estimates of droplet size and vaporization time do provide some evidence of the validity of this law even under transient temperature conditions [15, 21, 22]. In addition, Labowsky [19] showed that the d − law provides a reasonable prediction of the actual vaporization history of an interacting droplet, especially in the initial period of combustion. Considerable progress in going beyond the limitations of Labowsky’s model and its findings [19] can be found in the work of [20]. In principle, any more sophisticated model could be used as a basis for constructing the sectional evaporation coefficients. Inclusion of such details is likely to affect our results in a quantitative rather than a qualitative way [24]. In a similar manner, no separate energy conservation equation is solved for the spray as the current model assumes instantaneous thermal adjustment of the gas-liquid mixture to a common temperature; although this may not always be the case in transient situations [23]. The present analysis is therefore limited to fairly volatile fuels and small droplets for which the d − law is valid. Under these assumptions, the spray sectional momentum equations are ∂ur,j ∂t + ur, j ∂ur,j ∂r − uθ,j r = Fr,j + 1 Q̃j (S j,r − ur,jSj) (8) ∂uθ,j ∂t + ur,j ∂uθ,j ∂r + ur,juθ,j r = Fθ,j + 1 Q̃j (S j,θ − uθ,jSj) (9) The last term in the brackets on the RHS of equations 8 and 9 represents loss of linear momentum (ujSj) due to evaporation of droplets in section j, and the linear momentum (S j ) added to section j due to droplets from higher sections that are added to section j during their evaporation (see [16]). Here, Sj = −CjQ̃j +Bj,j+1Q̃j+1 (10)

Effect of Grouping of Fuel Droplets on a Flame Formed by an Oscillating Spray Jet

The sensitivity to the vaporization Damkohler number of the behavior of a co-flow laminar spray diffusion flame in an oscillating flow field is investigated. Droplet grouping induced by the host gas flow oscillations is accounted for. The effect of droplet grouping is described through a specially constructed model for the vaporization Damkohler number that responds to the proximity of the droplets as they cluster due to the spray-flow oscillations. A formal analytical solution is developed for Schwab-Zeldovitch parameters through which the dynamics of the spray flame front shapes and thermal fields are deduced. Computed results based on the solutions demonstrate how strongly the vaporization Damkohler number including droplet grouping effects impacts on the type of primary homogeneous flame formed and on the possible existence of multiple flame sheets as a result of dynamic changes from under- to over-ventilated flames as the flow field oscillates.