This content is not included in your SAE MOBILUS subscription, or you are not logged in.
Modeling the Effects of Drop Drag and Breakup on Fuel Sprays
ISSN: 0148-7191, e-ISSN: 2688-3627
Published March 01, 1993 by SAE International in United States
Annotation ability available
Spray models have been evaluated using experimentally measured trajectories and drop sizes of single drops injected into a high relative velocity gas flow. The computations were made using a modified version of the KIVA-2 code. It was found that the drop drag coefficient and the drop breakup time model constant had to be adjusted in order to match the measurements. Based on these findings, a new drop drag submodel is proposed in which the drop drag coefficient changes dynamically with the flow conditions. The model accounts for the effects of drop distortion and oscillation due to the relative motion between the drop and the gas. The value of the drag coefficient varies between the two limits of that of a rigid sphere (no distortion) and that of a disk (maximum distortion). The modified model was also applied to diesel sprays. The results show that the spray tip penetration is relatively insensitive to the value used for the drop drag coefficient. However, the distribution of drop sizes within sprays is influenced by drop drag. This is due to the fact that changes in drop drag produce changes in the drop-gas relative velocity. This, in turn, causes changes in the spray drop size through the drop breakup and coalescence processes. The changes occur in such a way that the net effect on the spray penetration is small over the tested ranges of conditions. These results emphasize that measurements of spray penetration are not sufficient to test and produce improved spray models. Instead, local measurements of drop size and velocity are needed to develop accurate spray models.
SPRAYS ARE INVOLVED IN many practical applications, including spray combustion in diesel engines and port fuel injection in spark-ignited engines. In diesel engines the combustion rate is controlled by the vaporization of the drops. In spark-ignited engines, atomization quality influences the mixture preparation. In these applications the atomization process has a strong influence on fuel vaporization rates because it increases the total surface area of liquid fuel greatly.
The fundamental mechanisms of atomization have been under extensive experimental and theoretical study for many years *. Information about the mechanisms of atomization is important because it is needed to optimize the performance of injection systems. Precise formulation of the drop drag and breakup processes is also essential for accurate computer modeling of sprays.
Computer models such as the time-dependent, three-dimensional computational fluid dynamics computer code, KIVA, are available to study engine sprays and combustion . In some modeling studies the liquid fuel is injected as discrete parcels of drops or “blobs”, whose characteristic size is equal to the orifice hole size of the injector and the injection velocity is determined from the injection rate [3, 4]. The injected liquid is then broken up into atomized droplets which exchange mass, momentum and energy with the chamber gas.
Two atomization models are currently available for the breakup computations: the Taylor Analogy Breakup (TAB) model [5, 6], and the surface wave instability (wave) model . The theoretical development of these models is based on linear theories, and the models contain adjustable constants that need to be determined from experimental data. The accuracy of these models is assessed by comparison with well characterized experimental data in the present study, and the comparisons also provide information about the model constants.
The TAB model is based on Taylor's analogy  between an oscillating and distorting drop and a spring-mass system. The external force acting on the mass, the restoring force of the spring, and the damping force are analogous to the gas aerodynamic force, the liquid surface tension force, and the liquid viscosity force, respectively. The parameters and constants in TAB model equations have been determined from theoretical and experimental results, and the model has been applied successfully to sprays by O'Rourke and Amsden .
The wave breakup model considers the unstable growth of Kelvin-Helmholtz waves on a liquid surface. Reitz  used results from a linear stability analysis of liquid jets to describe the breakup details of the injected liquid “blobs”. This stability analysis leads to a dispersion equation which relates the growth of an initial perturbation on a liquid surface of infinitesimal amplitude to its wavelength and to other physical and dynamical parameters of both the injected liquid and the ambient gas. The physical parameters in wave model are similar to those in the TAB model. This model has also been used successfully in engine spray computations .
In addition to the final size of atomized drops, the drop breakup time is an important parameter that must be specified by drop breakup models. in particular, the breakup time constant determines the mass change rate of a atomizing liquid drop undergoing stripping breakup. An initial perturbation level is also specified in the breakup models. This model constant has been used to account for differences between sprays from different injector geometries. For, example, a parameter called Amp0 is introduced in TAB model to account the initial oscillation amplitude of the liquid drops. An initial disturbance level also appears in the wave model as an initial wave amplitude.
In recent work by Diwakar et al. , measured liquid/vapor fuel distributions from an air-assisted injector were compared with computational results obtained using the TAB breakup model. Significant differences were observed between measured and calculated spatial structures within the sprays when the breakup model constants were varied. However, the selection of the model parameters such as breakup drop sizes, time constants and initial disturbance levels is difficult due to a lack of relevant experimental data.
In addition to the physics of the breakup model, another important part of spray models is the liquid drop drag coefficient. The drag effects the drop's acceleration, and hence its velocity and physical location as a function of time. In most spray modeling studies, the drop drag coefficient is specified as a function of the drop Reynolds number (based on the drop-gas relative velocity) using solid-sphere correlations . Some studies have included the effect of vaporization (blowing) on the drag coefficient . However, the effects of drop oscillation and distortion have not been considered previously.
In this paper, a new submodel is proposed to account for the effects of drop oscillation and distortion on the drop drag coefficient. The model uses the approach of the TAB model to estimate the distortion of drops in a high relative velocity flow. Recent experimental results of Liu and Reitz  are used to evaluate the drop drag model for drops undergoing breakup using both the TAB and wave breakup models. The drop breakup experiments are described first, along with other spray experiments used in the comparisons. Next, a brief review of the theories of the wave and TAB models is given. The measured drop trajectories are compared with those from the models using various model parameters. Finally, the effects of drop breakup and drop drag models on diesel spray predictions is discussed.
CitationLiu, A., Mather, D., and Reitz, R., "Modeling the Effects of Drop Drag and Breakup on Fuel Sprays," SAE Technical Paper 930072, 1993, https://doi.org/10.4271/930072.
- Reitz, R.D. and Bracco, F.V. “Breakup Regimes of Round Liquid Jets,” Encyclopedia of Fluid Mechanics, 1987.
- Amsden, A.A., O'Rourke, P.J., and Butler, T.D., “KIVA-II: A Computer Program for Chemically Reactive Flows with Sprays,” Los Alamos National Laboratory Report No. LA-11560-MS, 1989.
- Reitz, R.D. and Diwakar, R., “Effects of Drop Breakup on Fuel Sprays,” SAE Paper 860469, 1986.
- Reitz, R.D. and Diwakar, R., “Structure of High-Pressure Fuel Sprays,” SAE Paper 870598, 1987.
- O'Rourke, P.J. and Amsden, A.A., “The TAB Method for Numerical Calculation of Spray Droplet Breakup,” SAE Paper 872089, 1987.
- Taylor, G.I., “The Shape and Acceleration of a Drop in a High Speed Air Stream,” in The Scientific Papers of G.I. Taylor, ed. Batchelor G.K., Vol.III, University Press, Cambridge, 1963.
- Reitz, R.D., “Modeling Atomization Processes in High-Pressure Vaporizing Sprays,” Atomisation and Sprays Tech., vol.3, P.309-337, 1987.
- Gonzalez, M., Lian, Z., and Reitz, R.D., “Modeling Diesel Engine Spray Vaporization and Combustion, SAE paper 920579, 1992.
- Diwakar, R., Fansler, T.D., French, D.T., Ghandhi J.B., Dasch, C.J., and Heffelfinger, D.M., “Liquid and Vapor Fuel Distribution from an Air-Assisted Injector - An Experimental and Computational Study,” SAE Paper 920422, 1992.
- Liu, A.B. and Reitz, R.D., “Mechanisms of Air-Assisted Liquid Atomization,” Atomization and Sprays, Vol. 3, pp. 1-21, 1992
- Berglund, R.N. and Liu, B.Y.H., “Generation of Monodisperse Aerosol Standards,” Env. Sci. Tech., Vol.7, P.147, 1973.
- Liu, A.B., “Mechanisms of Air-Assisted Liquid Atomization,” MS Thesis, University of Wisconsin-Madison, 1991.
- Simpkins, P.G. and Bales, E.L., “Water-Drop Response to Sudden Accelerations,” J. Fluid Mech., Vol.55, No.4, P.629, 1972.
- Hiroyasu, H., and Kadota, T. “Fuel droplet size distribution in diesel combustion chamber,” SAE Paper 740715, 1974.
- Ranger, A.A. and Nicholls, J.A., “Aerodynamic Shattering of Liquid Drops,” AIAA, J., Vol.7, No.2, P. 285, 1969.
- Hinze, J.O., “Fundamentals of the Hydrodynamic Mechanism of Splitting in Dispersion Processes,” A.I.Ch.E. J., Vol.1, No.3, P.289, 1955.
- Ruman, M.A., “A Computational model for the Prediction of Droplet Shapes and the Onset of Droplet Breakup,” MS Thesis, Michigan Technological University, 1988.