Thermal ignition analysis of a monodisperse spray with radiation

Sazhin, Sergei; Gao, Feng; Heikal, Morgan; Goldfarb, Igor; Gol’dshtein, Vladimir; Kuzmenko, Grigory

doi:10.1016/s0010-2180(00)00237-6

Cited by 67 publications

(69 citation statements)

References 31 publications

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“…9, No. 1;2017 temperature has been assumed to be equal local temperature in the vicinity of droplet, then the evaporation time (that the authors of Sazhin et al (2001) obtained analytically from the model), agree with the evaporation time that predicted by CFD. The thermal radiation, for high temperature and large droplets cannot be ignored.…”

Section: The Delay Time In the Model Of Thermal Explosion Of A Gas MImentioning

confidence: 54%

“…Significant influence on the development of the method has been made by Bogolubov and Mitropolsky (1963). Another results of the theory of integral manifolds are presented by Mitropolsky (1973), and in Sazhin et al (2001) the MIM was applied to a specific problem of modeling of the ignition process in diesel engine.…”

Section: Thermal Explosion Of Monodisperse Spray Combustionmentioning

confidence: 99%

“…The relative error (%) in the delay time upper bound versus the initial radius of droplets and Relative error (%) in the delay time upper bound versus the number of dropelts per unit volume are presented in Figure . The next model that have been presented by the authors of (Babushok & Goldshtein, 1988;Gol'dshtein & Sobolev, 1992;Goldfarb et al, 1997;Goldfarb, Gol'dshtein, Kuzmenko, & Greenberg, 1998;McIntosh, Gol'dshtein, Goldfarb, & Zinoviev, 1998;Goldfarb, Gol'dshtein, Greenberg, & Kuzmenko, 2000;Sazhin et al, 2001; ) generalized the model of in such way that the model take into account the effect of thermal radiation of heat transfer between the droplet and gas in different way and more precisely. The main physical assumption of the model are: The contribution of the thermal radiation based on the P − 1 approximation for the thermal radiation transfer with Marshak boundary condition (Modest, 1993;Sazhin et al, 1996;Siegel & Howell, 2002;), the spray is monodisperse spray, the droplets are opaque, their surface are gray, and the radiative temperature T r is equal to the gas temperature T g , the Spalding number is small, the characteristic time of droplet t d and gas t g for typical diesel engine parameters satisfies the inequality t d << t g and the droplet heating can be neglected.…”

Section: The Delay Time In the Model Of Thermal Explosion Of A Gas MImentioning

confidence: 99%

“…The difference between the model presented by (Goldfarb, Gol'dshtein, Kuzmenko, & Sazhin, 1999;Sazhin et al, 2001)is the qualitative analysis. The last one (Sazhin et Let θ be the dimensionless gas temperature.…”

Section: The Delay Time In the Model Of Thermal Explosion Of A Gas MImentioning

confidence: 99%

“…The expressions a θi and b θi can be found in their explicit form in Sazhin et al (2001). Appropriate algebraic manipulations one can obtain the solution for θ 1 as: where…”

Section: The Delay Time In the Model Of Thermal Explosion Of A Gas MImentioning

confidence: 99%

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Mathematical Modelling of Spray Combustion-Numerical and Analytical Analysis with application to Engineering Science

Nave¹,

Ajadi²,

Gol’dshtein³

2016

APR

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In the present paper we applied two well-known analytical method to the problem of thermal explosion of monodisperse and polydisperse fuel spray. The methods are the method of integral manifold (MIM) and the homotopy analysis method (HAM). The MIM method used as a basic tools for the analysis of SPS system of ordinary differential equations which means that the physical/ mathematical model should contain a small parameter in the governing equations. The HAM is always valid no matter whether there exist small physical parameters or not in contrast to the classical perturbation methods which requires the existence of a small parameter in the system (in general this is not the case). According to the theory of HAM, the convergence and the rate of solution series are dependent on the convergent control parameter ℏ. This means that this parameter gives one a convenient way to adjust and to control the convergent region of the solutions. γ (conventional parameter of Semenov's theory of thermal explosion), the final dimensionless adiabatic temperature of the thermally insulated system after explosion. This parameter is small compared with unity for most gaseous mixture due to the high exothermicity and activation energy of the chemical reactionwhere ϵ d is the emissivity of the droplet surface ϵ 1,2 dimensionless parameters, introduced for the first time (Gol'dshtein, Goldfarb, Shreiber, & Zinoviev, 1996) and describe the relations between the thermo physical properties of the gas and liquid phases

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Section: The Delay Time In the Model Of Thermal Explosion Of A Gas MImentioning

confidence: 54%

Section: Thermal Explosion Of Monodisperse Spray Combustionmentioning

confidence: 99%

Section: The Delay Time In the Model Of Thermal Explosion Of A Gas MImentioning

confidence: 99%

Section: The Delay Time In the Model Of Thermal Explosion Of A Gas MImentioning

confidence: 99%

“…The expressions a θi and b θi can be found in their explicit form in Sazhin et al (2001). Appropriate algebraic manipulations one can obtain the solution for θ 1 as: where…”

Section: The Delay Time In the Model Of Thermal Explosion Of A Gas MImentioning

confidence: 99%

See 3 more Smart Citations