TY - JOUR

T1 - A probabilistic model of thermal explosion in polydisperse fuel spray

AU - Nave, Ophir

AU - Bykov, Vitcheslav

AU - Gol'Dshtein, Vladimir

PY - 2010/11/15

Y1 - 2010/11/15

N2 - This work is concerned with an analysis of polydisperse spray droplets distribution on the thermal explosion processes. In many engineering applications it is usual to relate to the practical polydisperse spray as a monodisperse spray. The Sauter Mean Diameter (SMD) and its variations are frequently used for this purpose [13]. The SMD and its modifications depend only on "integral" characterization of polydisperse sprays and can be the same for very different types of polydisperse spray distributions. The current work presents a new, simplified model of the thermal explosion in a combustible gaseous mixture containing vaporizing fuel droplets of different radii (polydisperse). The polydispersity is modeled using a probability density function (PDF) that corresponds to the initial distribution of fuel droplets size. This approximation of polydisperse spray is more accurate than the traditional 'parcel' approximation and permits an analytical treatment of the simplified model. Since the system of the governing equations represents a multi-scale problem, the method of invariant (integral) manifolds is applied. An explicit expression of the critical condition for thermal explosion limit is derived analytically. Numerical simulations demonstrate an essential dependence of these thermal explosion conditions on the PDF type and represent a natural generalization of the thermal explosion conditions of the classical Semenov theory.

AB - This work is concerned with an analysis of polydisperse spray droplets distribution on the thermal explosion processes. In many engineering applications it is usual to relate to the practical polydisperse spray as a monodisperse spray. The Sauter Mean Diameter (SMD) and its variations are frequently used for this purpose [13]. The SMD and its modifications depend only on "integral" characterization of polydisperse sprays and can be the same for very different types of polydisperse spray distributions. The current work presents a new, simplified model of the thermal explosion in a combustible gaseous mixture containing vaporizing fuel droplets of different radii (polydisperse). The polydispersity is modeled using a probability density function (PDF) that corresponds to the initial distribution of fuel droplets size. This approximation of polydisperse spray is more accurate than the traditional 'parcel' approximation and permits an analytical treatment of the simplified model. Since the system of the governing equations represents a multi-scale problem, the method of invariant (integral) manifolds is applied. An explicit expression of the critical condition for thermal explosion limit is derived analytically. Numerical simulations demonstrate an essential dependence of these thermal explosion conditions on the PDF type and represent a natural generalization of the thermal explosion conditions of the classical Semenov theory.

KW - Autoignition fuel spray

KW - Method of integral manifolds

KW - Sauter mean diameter

KW - Thermal explosion limit

UR - http://www.scopus.com/inward/record.url?scp=77957986615&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2010.07.078

DO - 10.1016/j.amc.2010.07.078

M3 - Article

AN - SCOPUS:77957986615

VL - 217

SP - 2698

EP - 2709

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 6

ER -