A Practical Calculation Method for Injection Pressure and Spray Penetration in Diesel Engines 920624
Spray penetration for Diesel injectors, where injection pressure varies with time during the injection period, was calculated. In order to carry out this calculation, the discharge coefficients of the needle-seat opening passage and discharge hole in orifice-type Diesel nozzles were investigated separately. Simple empirical correlations were obtained between these coefficients and needle lift. Then, by introducing these correlations, the injection pressure, which is defined as the pressure in the sac chamber just upstream of the discharge hole, was either derived from measured fuel supply line pressure, or predicted by means of an injection system simulation. Finally, based on the transient injection pressure, spray tip penetration was calculated by taking the overall line which covers the trajectories of all fuel elements ejected during the injection period. Discharge coefficient correlations, models for calculating injection pressure, and for spray penetration were validated by comparing the calculated and measured results of injection characteristics and spray penetration over a wide range of experimental conditions.
DIESEL SPRAY PENETRATION has been investigated by many researchers since the beginning of this century. Many theoretical and empirical correlations were recommended for its prediction. Schweitzer * examined the influence of injection pressure, and summarized the results in terms of a set of simple correlations. Later, Parks  added the effect of ambient temperature, and modified Schweitzer's correlations. Wakuri et al.  and Dent  derived their correlations from the theory of momentum conservation and the theory of two phase jets respectively, while Hay  surveyed many previous works and suggested a new correlation. These three correlations [3, 4 and 5] indicated that spray penetration is in proportion to the square root of time after the start of injection. Furthermore, Hiroyasu and Arai  paid a particular attention to the initial part of the spray at the beginning of the injection, and found that spray penetration is initially proportional to time. At later stages, it is proportional to the square root of time, as was pointed out by the previous researchers. The point connecting the two regions corresponds to the beginning of the breakup process, i.e. the breakup length. They obtained their correlations according to Levich's jet disintegration theory , and determined the coefficients from the results of an extensive experimental investigation.
In Diesel engines, the injection pressure in the sac chamber always varies temporally during injection. Its variation depends on the operating conditions and hydrodynamic characteristics of the injection system. The needle valve inside the nozzle also plays an important role in this phenomenon, especially during the onset and the end of injection. The transient and unstable nature of the injection process predominates the spray formation and development, as well as the atomization process.
Hiroyasu and Arai used a standard Diesel nozzle with a movable needle in their experiment , but constant line pressure was considered as the injection pressure because it is difficult to measure the sac chamber pressure directly. Though the difference between the line pressure and the real injection pressure is very small after the needle is totally opened, during the initial stage the injection pressure increases sharply from zero with the increase of needle lift, whereas the line pressure changes only slightly. In Eq.(1), an abnormally small velocity coefficient of 0.39 had to be used to fit the experimental results of initial penetration, because the line pressure was used as the injection pressure in the correlations. So far, the line pressure seems to have been accepted as the injection pressure by most engine researchers and designers just for convenience. Some of them related the variation of the line pressure to the transient spray characteristics or engine performance, another tried to predict spray penetration and/or other spray characteristics based on the average line pressure . The importance of the effects due to the transient injection pressure and its variation on Diesel spray transient behavior has not been properly recognized. As a result, most of the available correlations give poor agreement with the experimental results obtained under actual engine conditions. On the other hand, some numerical modeling of Diesel sprays has also resulted in large deviation between computational and experimental results . Therefore, the previous correlations are insufficient for estimating the spray penetration of a practical Diesel injection system. A new calculation method for spray penetration considering the effects of injection pressure variation and needle lift is necessary for Diesel engine design and improvement, as well as for comparison to numerical modeling results.
Injection pressure has been known as an important factor which primarily controls spray penetration and other spray properties. However, the tiny dimension of the inner passage inside the Diesel nozzle makes it almost impossible to correctly measure the injection pressure in the sac chamber. Woschni  performed a calculation program by which injection pressure and injection rate can be derived from the measurement results of line pressure. On the other hand, the injection pressure can also be obtained as one of the final results of an injection system numerical simulation. In both methods, the discharge coefficients of two reduction areas of the fuel passage in the nozzle, that is, the needle seat opening passage and the discharge hole, are necessary for solution of the flow equations in the nozzle. Although many correlations of discharge coefficient for steady-state flow through plain orifices have been suggested [11, 12], they do not include the effects of the transient variations in injection pressure and needle lift in the Diesel nozzles. Certainly the choices of constant discharge coefficient in Woschni's method and many other simulation models is not sufficient. In addition, the discharge coefficient of the seat passage has been neglected by many researchers.
In the present work, the authors firstly surveyed the typical geometry of the Diesel nozzles and derived a precise description of the minimum flow area of the needle seat opening passage (briefly, seat passage) as function of needle lift. In order to investigate the discharge coefficients of the seat passage and the hole separately, a special nozzle was used, in which the portion below the seat (including the sac chamber and the hole) was removed. By measuring the line pressure, needle lift and discharge flow rate from the seat passage exit, and deriving the pressure in the pressure chamber which is located upstream of the seat passage, the discharge coefficient of the seat passage was obtained. Then the same measurements were made for normal Diesel nozzles. The discharge coefficient of the hole was calculated from the measured injection rate and the pressure in the sac chamber. The latter was derived from the line pressure by applying the discharge coefficient of the seat passage. The empirical correlations for the two coefficients were obtained based on the results of experiments conducted over a wide range of conditions. By introducing these correlations into the equations for the nozzle, and taking into account the effects of supply line friction and cavitation, the injection pressure was calculated from either line pressure (measurement) or operating conditions (simulation). The results were verified by the evidence of good agreement between calculated and measured injection rates over all the conditions.
Finally, the Hiroyasu and Arai's Eqs.(1), (2) and (3) of spray penetration were applied to the fuel elements ejected at a different time intervals which corresponded to different injection pressures. The coefficients in these equations were properly modified by fitting with the measured results of penetration, which were obtained by the light sheet interception method . Spray tip penetration was defined as the curve enveloping the trajectories of all the elements because they overtake each other. The comparison between calculated and measured penetration showed a good correspondence over a wide range of conditions. It proved that the approach made in this study to estimate the injection pressure and spray penetration in Diesel engines is accurate, and provides a new tool for predicting the transient behaviors in injection system and spray formation.