Numerical Spray Calibration Process. ANSYS Inc. Pune, India. Laz Foley. ANSYS Inc. Evanston, IL

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1 ILASS Americas, 23 rd Annual Conference on Liquid Atomization and Spray Systems, Ventura, CA, May 2011 Numerical Spray Calibration Process Padmesh Mandloi *,Jayesh Mutyal, Pravin Rajeshirke ANSYS Inc. Pune, India Laz Foley ANSYS Inc. Evanston, IL Abstract Liquid sprays are involved in many engineering applications, including spray combustion in diesel and GDI engines, rocket engines, gas turbines, Selective Catalytic Reduction systems, spray painting etc. In all these applications, spray formation plays a critical role in determining the optimum performance of the component. For example, urea injection in a SCR system should result in proper atomization of the urea and water solution, producing droplets small enough to evaporate quickly but with momentum to sufficiently penetrate the exhaust system. CFD simulation of spray is rather complex since it has to accurately capture the effects of several physical behaviors like atomization, breakup and coalescence, interaction of spray on the continuum flow-field, evaporation, wall film formation and so on. Spray breakup models depend upon several factors and are primarily governed by Weber number. These empirical models require tuning of empirical model constants in order to accurately capture the spray formation process. The current study describes numerical approach of modeling sprays to obtain spray characterization results which are otherwise obtained using the Laser Sheet Imaging and Phase Doppler Particle Analyzer tests. Liquid spray is modeled using Discrete Phase Model (based on the lagrangian framework) in ANSYS FLUENT. Using a customized spray post-processing tool, spray characterization results such as penetration length, droplet diameters such as SMD, DV10, DV50 and other parameters like cumulative probability density plots are easily obtained. Spray breakup model constants are then tuned in order to obtain numerical results similar to the test data. This process is termed as numerical spray calibration. Spray validation studies are then presented where the accuracy of spray models is verified over a variety of spray scenarios. * Corresponding author

2 ILASS Americas, 23rd Annual Conference on Liquid Atomization and Spray Systems, Ventura, CA, May 2011 Introduction CFD simulation of spray is required in several applications including diesel and gasoline in-cylinder engines, liquid combustors, agricultural applications, aftertreatment systems etc. In all the applications listed above, the crux of the problem lies in accurately resolving the spray pattern and making the spray behave as close to the real-life scenario as possible. Multidimensional simulation of sprays; be it applied to diesel engines or liquid combustors, is still a big challenge. Although CFD claims to rely on physical principles rather than empirical formulas, and although there exist sophisticated theories for different types of sprays, the spray models currently available in literature will not work without adjustment of constants and fitting parameters based on detailed measurements [1]. However, since simulation of combustion and pollutant chemistry for example is not possible without correctly predicting the diesel or gasoline spray in an in-cylinder engine, it becomes essential to perform such studies. Tuning of the empirical constants applied to these different spray sub-models to achieve accurate spray behavior can be termed as "Numerical Spray Calibration". Numerical spray calibration is one of the initial steps in performing CFD simulation involving sprays. The paper starts with description of numerical spray calibration process, challenges and the different steps involved in the process. A brief overview of the spray measurement techniques is presented which highlights the need for accurate representation and interpretation of numerical results in a way that they can be easily compared against the standard test based results. This is followed by a section on the design and development of spray post-processing utility which helps in acquiring numerical spray results in some standard formats. Few validation studies representing different real-life applications are presented and conclusions are drawn. Numerical Spray Calibration Process Injectors are complicated devices, in the sense there are so many details that considering the effect of each of them while modeling the injector behavior without simulating each of these intricate details is quite very difficult. In a typical diesel fuel injector for example, details of the plunger, no. of nozzles, inlet pressure etc. can significantly change the spray behavior. Therefore, CFD spray modeling requires number of user inputs. In principle, one can use these geometrical details and setup the spray by using appropriate primary atomization model. Based on geometrical inputs and operating inputs, primary atomization model calculates the all droplet properties such as diameter, diameter distribution, velocity, mass flow rate, etc. There are several models available for modeling injector, for example Plain-orifice Atomizer model [2], Pressure-Swirl Atomizer [3] and many others. However, because of so many influencing geometrical parameters, none of these primary atomization models are popular for modeling injector. Other method is to define all droplet properties directly and bypass the primary atomization model. Though this is the most accurate method, it is hard to have all these properties unless one does the expensive experiments. In many studies [1, 4] separate injector CFD analysis is done to retrieve these properties. As described in Figure 1, CFD analysis provides detailed information on mass flow rate, velocities, cone angle. However, it does not provide any information about droplet diameter and diameter distribution. Therefore diameter is assumed to be equal to nozzle orifice diameter or somewhat decreased due to cavitation or turbulent effects. Figure 1. Numerical Spray Calibration. Second important aspect of spray modeling is predicting droplet breakup because of droplet gas interaction. Numbers of secondary atomization models are available. They include TAB (Taylor Analogy Breakup) [5], Kelvin Helmholtz wave model [6], Kelvin Helmholtz and Rayleigh Taylor (KH-RT) and Stochastic Secondary Breakup model (SSD) [7]. While these models can capture the important characteristics of the spray, they still need tuning for accurate prediction. This process of tuning the model against LDA / PDPA experimental measurements is shown in Figure 2. This process is termed as Numerical spray calibration. Figure 2. Numerical Spray Calibration. Let's take an example of The Taylor analogy breakup (TAB) model tuning. This model is based upon Taylor's analogy [8] between an oscillating and distorting droplet and a spring mass system. TAB model equa-

3 tion set, which governs the oscillating and distorting droplet, is solved to determine the droplet oscillation and distortion at any given time. When the droplet oscillations grow to a critical value the "parent'' droplet will break up into a number of smaller "child'' droplets. This critical value can be tuned correctly by changing model constant Y0. The effect of Y0 on SMD and penetration length is shown in Table 1. Bigger Y0 lowers the critical value and hence reduces the SMD and penetration length. Similar to Y0, other model constants are tuned to get measured SMD and penetration length. Table 2 shows the directional behavior of model constant with respect to spray patternation. Y0 SMD (m) Penetration Length (m) e-5 5.8e e-5 5.6e-2 Secondary Breakup Model Table 1. Effect of Y0 on SMD and penetration length. Constants Comments TAB Y0 SMD and Penetration Length Wave KH-RT B1 C L C 3 SMD and Penetration Length SMD and Penetration Length SMD and Penetration Length Figure 3. Schematic of Laser Sheet Imaging The Phase Doppler Particle Analyzer [9] measures particle size and velocities. These are point sampling devices. This means that these instruments focus on a sample of the total spray and use this sample size to extract information like average particle diameter, average velocity etc. Figure 4 shows a simple schematic of a PDPA system. PDPA technique allows to characterize spray in the form of beam SMD, DV10, DV50, DV90, Average Velocity and so on. These numbers can be spatially averaged along the beam or can be represented as a function of space along the beam direction. Table 2. Directional behavior of some model constant with respect to spray patternation. Spray Measurement Techniques The two most commonly used testing techniques for spray characterization are Laser Sheet Imaging (LSI) and Phase Doppler Particle Analyzer (PDPA). LSI is used to examine spray plume range and uniformity whereas PDPA is used in acquiring drop size and velocity data across the majority of spray area. The Laser Sheet Imaging technique [9] provides a non-intrusive method for measuring two dimensional spray plume concentration distribution. In LSI technique, scattered light intensity is measured as the particles pass through a nominally two dimensional laser sheet. This light intensity is either proportional to either droplet surface area or drop volume. After acquiring many instantaneous images, an average spray distribution is determined. The LSI technique is suitable for low flow, small droplet shaped (round or hollow) sprays. Figure 3 describes a simple schematic of LSI. Figure 4. Schematic of PDPA The spray post-processing utility described in the following section tries to mimic the PDPA technique of spray characterization. Process of getting images that can be directly compared with the LSI images is also described.

4 Spray Post-processing Utility As shown in Figure 5, in experimental spray calibration, particle data is measured at different planes or beams passing through spray. This data is then reduced to calculate the SMD, velocity and other data over the plane or beam. These studies also provide lateral distribution. Exactly similar data processing is needed for numerical spray calibration. Experimental data on beam /plane is compared with numerical data on corresponding beam/ plane to arrive to better empirical model constants. As shown in Figure 6, a FLUENT based utility is developed which allows user to define various postprocessing beams or planes similar to LDA / PDPA measurements. This utility record all particles intercepted by these beams or planes or sectors and provide (a) Beam averaged SMD, DV10, DV50, DV90 and particle velocity. (b) Distribution of SMD, DV10, DV50, DV90 and particle velocity along the beam length (c) Number density on beams. As this utility is User Defined Function (UDF) based, existing output parameter can be modified and new output parameters can be added quickly. The data generated is exactly same as that of experimental measurements which enables quick comparison and tuning. and m below injection location origin are assumed here. These beams intercept the spray obliquely. The SMD and velocity distribution along the laser beams can be plotted easily. Similarly the number density can be estimated using the tool and compared with that obtained from the PDPA tests. Figure 5. Schematic of LDA / PDPA measurements. Figure 7. Results from spray post processing utility Validation Studies Figure 6. FLUENT based utility for numerical spray calibration. Figure 7 below shows some representative results from the spray post-processing tool. Two laser beams, beam-1 and beam-2 of radius 2.5 mm, defined at 0.07m After having established a process for numerical calibration, the current section focuses on some validation studies to verify the accuracy of the solver using the best practices developed so far.

5 Case-1 Case-2 Case-3 Gas Temperature (K) Gas Pressure (MPa) Particle Mass Flowrate (g/s) Nozzle Diameter (mm) Injection rate (ms) Table 3. Experimental Parameters Case-1 Case-2 Case-3 Droplet Diameter (mm) Injection Velocity (m/s) Particle Mass Flowrate (g/s) Initial Spray Angle (deg) Table 4. Particle Injection Parameters Comparisons were made with experimental data for solid cone sprays of Hiroyasu and Kadota [10]. Table 3 describes the experimental parameters for all the three cases. Cases 1-3 differ in chamber pressure. These chamber pressures of 1.1, 3.0 and 5.0 MPa were set as initial conditions for the stagnant gas. The spray models also need inlet conditions for the spray, i.e., the drop size, inlet velocity, spray angle etc. at the injector nozzle exit. The initial droplet diameter was set equal to the experimental nozzle diameter (blob method). The conservation of mass allows to obtain the injection velocity U inj of the blobs. m U = ρ π D 4 Where m is the particle mass flow rate, ρ is the liquid density and D is the nozzle diameter. Similarly, the initial spray angle θ is derived based on empirical formulation [11] where θ is a function of gas density, liquid density and nozzle diameter and length. Table 4 presents the particle injection parameters for all the three cases. The computational domain consisted of a cylindrical region with dimensions 30mm x 100 mm with one-hole injector at the top center, directed in axial direction. Air in the cylindrical domain was modeled as ideal gas. Standard k-ε model was employed. Energy equation was not solved. C 12 H 26 was used as injected liquid with a density of 840 kg/m 3 and surface tension of kg/s 2. All the walls of the cylindrical domain were modeled with free slip condition. The flow was assumed to be stagnant to begin with. The initial values of k and eddy viscosity ratio were set as m 2 /s 2 and 1 respectively. A medium size (with 2.5 mm) structured mesh (O type Grid) was generated in the cylindrical domain. Figure8 shows the computational grid. The first simulation was performed with Wave breakup model (B0 = 0.61, B1 = 10). Figure 9 shows the comparison of penetration length for case-1 with experimental data. The simulated trend closely follows the test data till about 1 ms after which faster breakup leads to under-prediction in breakup length. In order to improve the accuracy of predicted results several different trials were made. Since breakup time is directly proportional to constant B1, larger B1 would mean larger breakup time and hence larger penetration length B 1 a Simulation was performed with B1 = 18 which showed marginal improvements in the prediction. The default drag law is based on the empirical correlation by Morsi and Alexander, which assumes spherical shape of the particles. For high speed sprays, particles don t retain their spherical shape and the non-spherical shapes need to be taken into account. Dynamic drag law, which accounts for distortion of particle shape based on the spring-analogy, was considered next. No perceptible improvement in accuracy was found as a result of using this model since the particle velocities were not too high. KH-RT breakup model, which accounts for both KH (Kelvin Helmholtz) and RT (Ray-

6 leigh Taylor) type instabilities was tried next. Penetration length predictions with this model were better than that with just the Wave breakup model although marginally. In the Wave and TAB models, the number of child droplets is fixed. The new Stochastic Secondary Breakup (SSD) model treats breakup at high Weber numbers as a discrete random event resulting in a distribution of diameter scales over a range. Using the SSD model, the penetration length matched very well up to about 15 to 20 ms after which it was under predicted. This prediction can be improved by fine tuning the default model constants. Finally the effect of collision model was considered. With collision model turned off, particles, even very close to each other would not collide and coalesce and grow in size. This would result in significantly faster decay of particle sizes and therefore much shorter penetration length. Collision model, therefore is very critical to accurate capture the spray shape. Collision models are prone to grid-dependency issues, therefore it is important to decide a mesh size first and then tune the other parameters to get reasonable results. Figure 10 shows penetration length results from all the different simulations done for case-1. Figures 11 and -12 show effect of the same parameters on penetration length for the other two cases; case-2 and case-3 respectively. The same trends, as observed in case-1 can be seen in case-2 and case-3. Figure 9. Comparison of penetration length, case-1, Hiroyasu and Kadota Figure 10. Effect of different breakup models on penetration length prediction, case-1, Hiroyasu and Kadota Figure 8. Comparison of penetration length, Case-1, Hiroyasu and Kadota Figure11. Effect of different breakup models on penetration length prediction, case-2, Hiroyasu and Kadota

7 Summary Figure 12. Effect of different breakup models on penetration length prediction, case-3, Hiroyasu and Kadota The validation results so far presented nonevaporating sprays. Simulated results were next compared with test data for a real life, multi-hole injector of a GDI engine. The computational domain consisted of a cylindrical region of size 240 mm x 80 mm. Structured O-type grid was created with an average mesh size of 2.5 mm. N-heptane (C 7 H 16 ) was used to represent gasoline fuel. The density and viscosity of this liquid were set as 682 kg/m 3 and kg/m-s. Cylinder temperature and pressure were set as 298 K and 100 KPa. Realizable k-epsilon turbulence model was used. A trapezoidal shape injection velocity curve was approximated to account for the injection pulse. KH-RT break-up model, with dynamic drag law and collision model were used in the simulation. Spray model results were post processed at a plane 50 mm from the tip of the injector. Spray post-processing tool, described in the above section was used for estimating SMD, penetration length and DV90 values. A virtual disc of 4 mm thickness at 50 mm from the tip was assumed to capture particle data and convert them in the form of SMD, DV90 and penetration length. Table 5 below shows the comparison of measured data with the simulated one. The agreement between the test data and the simulated results was found to be reasonable in the light of quite a few uncertainties related to the input data provided. Test Results Simulated Results Penetration length at 3.0 ms (mm) SMD (µm) DV90 (µm) An attempt has been made in the paper to address the difference issues and challenges while performing numerical simulation of sprays. The process of numerical modeling of sprays is described along with the assumptions that one has to make. Since spray sub models are empirical and numerical modeling involves issues related to grid dependency, time-step size dependency, issues related to solver etc., it becomes important to tune all these parameters to accurately represent reallife spray behavior. Studies involving tuning these parameters and model settings can be termed as numerical spray calibration. Post-processing the spray data in a manner that allows easy co-relation with spray characteristics is very important for numerical spray calibration. A post-processing tool addressing these needs are described which tries to replicate real-life PDPA and LSI testing techniques. Validations for non-evaporating and evaporating sprays are presented to ascertain the efficacy of the solver to resolve the complex physics behind spray development. Acknowledgement The authors would like to extend their thanks to Frederick Bedford for his support and insightful ideas throughout the creation of this paper. References 1. Waidmann, W., Boemer, A., and Braun, M., Adjustment and Verification of Model Parameters for Diesel Injection CFD Simulation, SAE (2006) 2. Soteriou, C., Andrews, R. and Smith, M. Direct Injection Diesel Sprays and the Effect of Cavitation and Hydraulic Flip on Atomization. SAE Technical Paper Series , (1995). 3. Schmidt, D. P., Nouar, I., Senecal, P. K., Rutland, C. J., Martin, J. K. and Reitz, R. D. Pressure-Swirl Atomization in the Near Field. SAE Paper , SAE, (1999) 4. Das, S., Chang, S., and Kirwan, J., Spray Pattern Recognition for Multi-Hole Gasoline Direct Injectors Using CFD Modeling, SAE (2009) 5. O Rourke, P.J, and Amsden, A.A., The TAB Breakup Model for Low Injection Pressures SAE Paper , (1987). 6. Reitz, R.D., Modeling Atomization Processes in High Pressure Vaporizing Sprays, Atomization and Spray Technology, pp

8 7. Apte, et.al., LES of atomizing spray with stochastic modeling of secondary breakup, IJMF 29, 2003, pp Taylor, G. I. The Shape and Acceleration of a Drop in a High Speed Air Stream. Technical report, In the Scientific Papers of G. I. Taylor, ed., G. K. Batchelor, (1963) 9. ng.asp 10. Hiroyasu, H. and Kadota, T., Fuel Droplet Size Distribution in Diesel Combustion, SAE , (1974) 11. Tanner, F. X., Liquid Jet Atomization and Droplet Breakup Modeling of Non Evaporating Diesel Fuel Spray, SAE Technical Paper Series, , (1997)