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Turbulent Structure of the Diesel Spray

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Modelling Diesel Combustion

Part of the book series: Mechanical Engineering Series ((MES))

Abstract

Holographic interferometry has been applied to the study of concentration and temperature distribution in transient vaporizing non-burning and burning fuel sprays in a quiescent bomb. Semi-theoretical relations have been obtained in this chapter to describe the axial and radial variations of concentration in the vaporizing non-burning spray and to evaluate the penetration of sprays and air entrainment in the free and wall jet regions of non-burning and burning sprays. The movement of the “tail” of the spray in the post-injection period is studied. The data is presented for species concentration and temperature profiles within the burning spray. The equations form the basis for building the phenomenological models of ignition delay, emissions, and heat release rate in the next chapters.

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Abbreviations

A f :

= 0.5 (experimental), the proportionality constant of Ricou-Spalding relation of the ratio of air entrainment rate to fuel injection rate with the ratio of axial distance to equivalence diameter of the nozzle hole whereas proposed by Spalding was 0.32 (−)

A w :

similar to the Af proposed by Ricou and Spalding for free spray, a constant for spray along the wall, 0.95 (−)

C :

concentration (−)

C f :

concentration of fuel (−)

\(C_{f_{\max } }\) :

concentration with axial distance, x (−)

C R,L. :

refers to the mixture fraction at rich limit combustion (−)

d e :

orifice equivalent diameter and for the non-burning jet is defined as do ╳ [density of injected fuel/density of air in Bomb]1/2 (m)

de :

equivalent diameter of the nozzle hole (m)

H :

distance from the nozzle hole to the plate on which the spray impinges at a right angle (normally) (m)

K b :

combined Gladstone-Dale constant for burned products (m3/kg)

m :

mass entrained (kg)

\(m_a^{\prime} {\text{and }}m_o^{\prime}\) :

rate of air mass entrained into the jet, and the rate of mass flow of the jet fluid through the orifice respectively (kg/s)

M b :

average molecular weight of the products of combustion at the rich limit (kg/kmol)

M f :

molecular weight of fuel (kg/kmol)

n :

refractive index (−)

p :

pressure (Pa)

r :

radius at any x position from the nozzle hole (m)

R 0.5 :

radius at which the concentration has half its maximum value (m)

r 0.5 :

radius at which concentration of fuel drops 50%, used for non-dimensionalizing r (m)

S :

penetration along the wall (m)

s :

distance of the wall jet from the point of impingement (m)

t :

time (s)

T :

temperature (K)

t imp :

time after jet impingement (s)

t inj :

injection period (s)

U j :

velocity of fuel at the nozzle hole (m/s)

w :

radius of the free jet at x = H (m)

x :

axial distance in the free spray along the centre line of the nozzle hole from the nozzle hole (m)

x o :

distance from the orifice beyond which \(C_{f_{\max } }\) with the axial position is decaying (m)

y :

distance perpendicular to the impingement plate (m)

y :

height of wall jet (m)

y :

height in the free spray at a radial distance of s from the point of impingement (m)

y 0.5 :

height at which concentration of fuel drops 50%, used for non-dimensionalizing y (m)

z :

constant of proportionality in equation (4–7) =0.75

δ :

location of the virtual source inside the nozzle at δ/de = 2.3 (m)

\(\theta_{{\text{cone}}} /2\) :

half jet angle, tan(cone angle/2) = 0.22 (°)

ρ a :

density of air (kg/m3)

ρ f :

density of fuel (kg/m3)

Φ:

mixture fraction (−)

\(\infty\) :

surroundings

r :

considered a point in the jet

f :

fuel vapour

a :

air

f :

free jet

f :

fuel

imp:

impingement time

inj:

end of injection

max:

maximum of the variation, for example, of the concentration profile of fuel over a section at an axial distance x or distance along the wall, s

r :

any point in burning spray

w :

wall jet

. :

rate with respect to time

’:

rate with respect to time

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Authors and Affiliations

  1. IIT Kanpur, Kanpur, India

    Dr. P. A. Lakshminarayanan

  2. Kirloskar Oil Engines Limited, Pune, India

    Yogesh V. Aghav

Authors
  1. Dr. P. A. Lakshminarayanan
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  2. Yogesh V. Aghav
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Correspondence to P. A. Lakshminarayanan .

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Lakshminarayanan, P.A., Aghav, Y.V. (2022). Turbulent Structure of the Diesel Spray. In: Modelling Diesel Combustion. Mechanical Engineering Series. Springer, Singapore. https://doi.org/10.1007/978-981-16-6742-8_4

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  • DOI: https://doi.org/10.1007/978-981-16-6742-8_4

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