Interpretative Review of Diesel Spray Penetration Normalized by Length and Time of Breakup (Similarity Law of Diesel Spray and Its Application)

Abstract

Tip penetration of diesel spray is one of the most useful parameters to evaluate diesel combustion dynamics. It has strong relationships with ignition delay, premix/diffusion combustion and engine performance, including exhaust emissions. To discuss general combustion physics in various size sprays, non-dimensional expression of spray tip penetration is reviewed. Length and time of injected fuel jet breakup can be considered as characteristic length and timescale of diesel spray. Then, normalized penetration by length and time of breakup was proposed for the scaling of various diesel sprays. Using the proposed scaling method and similarity law, tip penetrations of various size sprays are collapsed into one simple expression. It becomes a base of similarity law of diesel spray. For example, local or average A/F is uniquely expressed by the normalized length and time of breakup. Penetration of a wall impingement spray is also expressed uniquely by this normalization method and physical parameters affecting the wall impingement spray are explained. Injection rate shaping effect at an initial stage of injection is clearly demonstrated by using this scaling. Further, mixing degrees of diesel spray at an ignition timing and in a combustion phase can be reasonably explained by the equivalence ratio change with non-dimensional elapsed time after injection start.

Experimental investigation on effect of gas/spray interactions on transient diesel spray behaviors

“…For the spray development, it is well accepted that the spray penetration can be divided into two stages, in spite that the physical understandings on the transition time are different. 1,5,6 The widely used model proposed by Hiroyasu and Arai 5 termed the transition time breakup time ( t breakup ), where the liquid column starts to breakup. In their model, the penetration length ( S ) is linear with the time ASOI ( t ) in the first stage and the square root of time ASOI, once the boundary conditions are given, as shown in equations (1) to (3).…”

“…[2][3][4] Based on the experiment results and theoretical analysis, several correlations have been proposed in order to predict the penetration length. 1,5,6 Previously, a number of research were mainly focusing on the global spray process over a wide range of boundary conditions, including P inj , ambient density (r ambient ), fuel properties, and nozzle geometry and so on. 4,[7][8][9][10][11][12][13][14][15] Herein, the main focuses are the characteristics of spray-induced shock waves and their effects on the spray development.…”

“…In diesel engines, the spray quality plays an important role in influencing the performance. In spite that massive studies on diesel fuel spray characteristics have been carried out in the past decades, 1 it is worth continuing with the help of advanced optical diagnostics techniques and modeling tools. Nowadays, increasing injection pressure ( P inj ) is still an effective way to improve the emissions.…”

Arrhenius type empirical ignition delay equations based on the phenomenology of in-cylinder conditions for wide operating ranges in modern diesel engines

“…t: Total duration of ignition delay [s] t c : Chemical process duration of ignition delay [s] t b : Breakup time of liquid fuel jet [s] The breakup time of liquid fuel jet, t b [s] is calculated with the modified Hiroyasu and Arai penetration equation, [64][65][66][67] as shown in equation ( 6): The equation includes the fuel injection pressure, empirically verified in a rage of current common rail injection system.…”

“…2u: Cone angle of the fuel spray [degrees] The spray tip distance, x [m] at the time, t [s] from SOI [64][65][66][67] and the cone angle of the fuel spray, 2u [degrees] 64,69 are obtained as follows:…”