AUTHOR=Ailaboina Akhil , Saha Kaushik 

TITLE=On Modeling of Spray G ECN Using ROI-Based Eulerian-Lagrangian Simulation

JOURNAL=Frontiers in Mechanical Engineering

VOLUME=8

YEAR=2022

URL=https://www.frontiersin.org/journals/mechanical-engineering/articles/10.3389/fmech.2022.880635

DOI=10.3389/fmech.2022.880635

ISSN=2297-3079

ABSTRACT=<p>A numerical study has been carried out to understand the effects of Unsteady Reynolds Averaged Navier-Stokes (standard k ― ε and RNG k ― ε model) and large eddy simulations (LES) on a multi-hole gasoline direct injection (GDI) system. The fuel injector considered in this study is the Spray G nozzle from the Engine Combustion Network (ECN). A blob injection model, based on empirical rate of injection (ROI) profile, is considered in this study. The latest data on spray penetrations from Engine Combustion Network is used for model validation along with experimental findings on suction velocity and local droplet diameter. The spray breakup is simulated by using the KH-RT breakup length model. The turbulence model constant <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, is tuned to match with the experimental data of liquid and vapor penetrations in simulations while using the standard <italic>k-ε</italic> turbulence model. On the other hand, the Kelvin-Helmholtz breakup model time constant <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> and Rayleigh Taylor breakup length constant <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are tuned for the RNG k ― ε turbulence model. From this work it is observed that by increasing the breakup length model constants <inline-formula id="inf4"><mml:math id="m4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the radial dispersion of the spray increases, and the extent of breakup is lowered. The set of optimized model parameters used with RNG <italic>k - ε</italic> is also used for LES modeling studies with different sub-grid models. The spray penetrations with standard k ― ε turbulence <inline-formula id="inf5"><mml:math id="m5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1.44</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> model are reported underpredicting, and the RNG k ― ε and LES sub-grid models predicted well with the latest and recommended data from ECN. In terms of gas axial velocity comparison, the standard <italic>k-ε</italic><inline-formula id="inf6"><mml:math id="m6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1.44</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> simulation setup does not perform as well as the simulation setups using RNG <italic>k-ε</italic> and LES turbulence models (with breakup parameters: <inline-formula id="inf7"><mml:math id="m7" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> = 16 and <inline-formula id="inf8"><mml:math id="m8" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> = 32). However, the standard <italic>k-ε</italic><inline-formula id="inf9"><mml:math id="m9" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>1.44</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> simulation setup perform better than the simulation setups using RNG <italic>k-ε</italic> and LES turbulence models (with breakup parameters: <inline-formula id="inf10"><mml:math id="m10" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> = 16 and <inline-formula id="inf11"><mml:math id="m11" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> = 32) when it comes to predicting local droplet diameter at 15 mm downstream of the injector tip. A parametric study is also performed considering the geometry of the stepped holes in the computational domain. The rate of injection based simulation is initiated at the end of the smaller hole. The case including the stepped holes led to over-prediction compared to the case with the usual computational domain (i.e., without the stepped holes), in terms of spray penetrations, but exhibited higher levels of fluctuations in the spray morphology. Finally, parametric studies were carried out to understand the relative importance of the individual spray sub-models (breakup, evaporation and collision) and the results are conclusive that for a spray simulation the breakup models are the dominant factors.</p>