In my opinion, absolutely not. Either for Diesel or GDI applications, the use multinjection strategies cannot allow approaching steady state flow conditions. Pilot, main and post injections on Diesel are used to control combustion rate and noise in automotive applications; these events can be as short as 100 micros, preventing from achieving both full needle lift and flow full development. Further, the multiple injection are used to control the shape of the injection rate in the single event, the opposite in concept of steady state conditions. For GDI applications, with different goals that are mainly related to the jet penetation control in stratified charge operation, the use of multiple injection is nowadays diffused as on of the most promising technique.

Thank you for this complete answer with which I agree. Indeed, in the literature, CFD studies implying breakup models show that the transient part of the spray development is usually hard to predict accurately, when comparing to experimental data. Of course, CFD implies other problems but this is one of the causes of this discrepency...

Also, I spoke with a colleague who made an experimental study on the injection rail and injector for this type of strategies using short injections. In addition to the needle lift problem well presented by L. Postrioti, there is also some pressure waves travelling in the system which can interact with the next injection, in particular with the injection rate. This phenomenon could have also an influence on the breakup rate through the injection velocity.

Speaking with an other investigator, he showed me that partial needle lift also appear to have a great influence on the turbulence inside the nozzle. As this turbulence is recognized as one of the causes of first atomization, in my opinion, this should have a significant influence on the droplet breakup.

Hello,

considering the velocity ranges in modern injectors (100m/s in GDI and several m/s in diesel) the assuption that heat transfer is much slower than atomization processes may hold. Of course that applies to the injector hole and close-to-nozzle regions in a first order approach. Clogging and other cracking processes show that thermal modification of fuel also takes places but concerns wall contact and large time scale beahaviour. So, if a heating of the fuel does takes place in the injector and must be taken into account when considering fuel properties (viscosity and surface tension which are highly dependent on temperature for most fuels), the atomization process itself may be considered isothermal.

hope it helps, good research

@Luis Very good analysis! However, the assumption that the heat transfer is much slower than the atomisation processes may not hold in view of heat transfer through semi-infinite medium. Liquid fuels are normally injected into an elevated combustion-chamber temperature, order of 10^3 K, to maintain a desirable homogeneous combustible mixture – liquid vapour and air. Prior to breakup, the liquid jet is in direct contact with the hot ambient, which may increase the liquid jet surface temperature down stream. Moreover, it has been shown, from experimental observations, that the jet breaks down stream of the nozzle. It's well established that the surface tension dictates the interfacial breakup mechanisms. Hence thermal modification of the jet surface would result in spatial variation of surface tension, since the surface tension is temperature-dependent. Of course, the thermal penetration, within the jet surface, is expected to be faster compare to the jet breakup time. Therefore, the consideration of the atomisation process (namely primary atomisation) may not be appropriate.

  L Le Moyne (2010)  Trends in atomization theory International Journal of Spray and Combustion Dynamics 2:  1.  49-84.

You are right, anyway if the atomisation process was perfectly well known models would probably be more accurate. As i said before, in a first approach temperature effects seem to be second order, but it is true that droplets having reached outer zones of spray and particularly those close to flame in late steps of diesel-type injection can be heated sensibly and affect physical and chemical properties (e.g. soot formation). Some years ago i had suggested that new models in atomisation should consider thermal effects :

best regards