Study of mass and momentum transfer in diesel sprays based on X-ray mass distribution measurements and on a theoretical derivation

In this paper, a research aimed at quantifying mass and momentum transfer in the near-nozzle field of diesel sprays injected into stagnant ambient air is reported. The study combines X-ray measurements for two different nozzles and axial positions,
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  1 Exp Fluids (2011) 50:233  – 246, DOI 10.1007/s00348-010-0919-8 STUDY OF MASS AND MOMENTUM TRANSFER IN DIESEL SPRAYS BASED ON X-RAY MASS DISTRIBUTION MEASUREMENTS AND ON A THEORETICAL DERIVATION. J.M. Desantes, F.J. Salvador (*), J.J. López, J. De la Morena. CMT-Motores Térmicos, Universidad Politécnica de Valencia, Camino de Vera s/n, E-46022 Valencia, Spain (*) Corresponding author: Dr. Francisco Javier Salvador Telephone: +34-963879658 FAX: +34-963877659 In this paper a research aimed at quantifying mass and momentum transfer in the near-nozzle field of diesel sprays injected into stagnant ambient air is reported. The study combines x-ray measurements for two different nozzles and axial positions, which provide mass distributions in the spray, with a theoretical model based on momentum flux conservation which was previously validated. This investigation has allowed the validation of Gaussian profiles for local fuel concentration and velocity near the nozzle exit, as well as the determination of Schmidt number at realistic diesel spray conditions. This information could be very useful for those who are interested in spray modelling, especially at high pressure injection conditions. Keywords: Diesel sprays, near field, Schmidt number, concentration, modelling,  x-ray  2 List of symbols  A Outlet hole section. C (x,r) Local spray mass concentration. C  v (x,r) Local spray volume concentration. C  axis  (x) Concentration at a determined axial position of the spray.  D  Mass diffusivity.  I X-ray beam intensity after passing through the spray.   I  0   X-ray beam incident intensity. i Counter of Taylor’s series.    j Counter used in the determination of the Mean Squared Deviation (MSD) between PDPA data and prediction by radial profiles. k Constant used in fitted Gaussian profiles.  M’    Projected mass obtained from x-ray measurements. o.  M    Momentum flux at the nozzle orifice outlet. a m  Air mass.  f  m  Fuel mass.  f . m  Fuel mass flow rate.  MSD Mean Squared Deviation between PDPA experiments and theoretical radial profiles.  p, q Counters in the numerical procedure for determining the optimal Schmidt number.  N   Number of terms in the Taylor series. n r   Number of measuring points in the radial direction. n  x  Number of measuring points in the axial direction. n ex  Number of measurements from PDPA. P back    Backpressure.  P in   Injection pressure.  3 r Radial coordinate. r  1   Radial position of the x-ray beam at the central plane of the spray. r  1/2   Radial position at which local spray velocity decreases until a value of 0.5· U  axis .    R Radius of the spray defined from velocity profile.  R m   Radius of the spray defined from concentration profile. S Spray tip penetration. Sc Schmidt Number. t Time from the start of injection. U  axis (x)   V elocity at the spray’s axis.   U  o Orifice outlet velocity. U(x, r) Local spray velocity. U  ex (x  j  ,r   j ) Experimental local velocity value from PDPA measurements at experiment  j . U  mo (x  j  ,r   j ) Local velocity value estimated form a theoretical radial profile at experiment  j . V  a Local volume occupied by air. V   f Local volume occupied by fuel.  x  Axial coordinate.  z Axial perpendicular coordinate used in the experimental x-ray measurements. Greek symbols:     Coefficient of the Gaussian radial profile for the axial velocity. ε  Mean deviation in the prediction of  M’  .   eq   Equivalent diameter.   o   Outlet diameter of the nozzle’s orifice.       Local spray density defined as a f a f  m mV V        .  4     L  Local fuel density defined as  f  La f  mV V        .    a  Ambient density.     f    Fuel density.   Kinematic viscosity.    Pi number.   m   Spray cone angle defined from mass distribution.   u   Spray cone angle defined from velocity distribution.  5 1. Introduction Despite being used in many industrial applications, the study of sprays has always been difficult due to the complex phenomena involved: atomization, mixing, coalescence, transfer of mass and momentum and evaporation (Lefèbvre 1989, Dumouchel 2008). This complexity is accentuated when studying sprays in direct injection diesel engines because of the high frequency transient operation and the small characteristic injection time and length (~1 ms and 25 mm). In such adverse conditions from the point of view of experimentation, the spray characteristics that can be measured are quite limited, especially in the densest part of the spray (near-nozzle region). The most typical characteristics are spray tip penetration and spray cone angle (Hiroyasu and Arai 1990; Naber and Siebers 1996; Way 1997; Roisman et al . 2007), which are macroscopic characteristics, and droplet velocity and droplet diameter, which are microscopic features (Wu et al.  1986; Jawad et al.  1992; Roisman and Tropea 2001; Subramaniam 2001). Nevertheless, in the studies available in the literature, the microscopic features are normally measured for axial positions far from the nozzle orifice, where local density in the spray has decreased due to air entrainment. This is especially true when the characterization is made by means of Phase Doppler Particle Analyzer systems (PDPA), which cannot work properly if droplet concentration is higher than a given threshold. In the last years, new and original techniques have been developed, helping to get further information about spray structure. As an example, x-ray measurements have shown to be useful in order to obtain information about mass distribution in the dense primary break-up (Leick et al. 2007; Tanner et al. 2006; Ramirez et al.  2009). As a consequence, in some cases, microscopic measurements are becoming as reliable as macroscopic ones, so that the relationship existing between them can be properly studied. One of the key parameters that relate microscopic and macroscopic characteristics of the spray is momentum flux. It is considered by several authors as one of the most important parameters governing the spray dynamics (Way 1997; Cossali 2001, Payri, F. et al.  2004; Desantes et al.  2006a). Momentum flux is a direct function of effective flux velocity at the orifice outlet, fuel density and effective diameter of the nozzle orifice and it can be properly measured using a suitable methodology (Payri, R. et al.  2005).
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