Modeling of Diesel Fuel Spray Formation in OpenFOAM

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1 Modeling of Diesel Fuel Spray Formation in OpenFOAM Anne Kösters (Chalmers Univ of Technology) Anders Karlsson (Volvo Technology Corporation)

2 Motivation Sprays are involved in many applications (internal combustion engines, exhaust aftertreatment, gas turbines ) CFD is an increasingly used tool in the development of these applications Spray and combustion models include many sub models Numerical unrobustness & many tuning parameters is an issue

tool in the development of these applications Spray and combustion models

3 Spray phenomena breakup evaporation and heat transfer droplet drag spray induced turbulence combustion

4 parcels

5 Spray Modeling - Shortcomings McKinley & Primus* cell widths are large and [ ] inadequate for capturing the strong gradients in velocity, temperature and fuel vapor concentration. This [leads] to under prediction of gas velocities and over prediction of gas temperatures within the spray Grid dependence Time step dependence Robustness Tuning parameters (sub models) *McKinley, T.L. & Primus, R.J., Three dimensional calculations of of air motion, sprays and combustion in in a quiescent Direct-Injection Diesel engine. ASME paper 90-ICE-2, 1990.

This [leads] to under prediction of gas velocities and over prediction of gas temperatures within the spray Grid dependence Time step

6 Work that has been done CERC McKinley, T.L. & Primus, R.J., ASME paper 90-ICE-2 (submesh spray model) Abraham, J., SAE technical paper (at least 4 cells needed in the orifice) Wan, Y.P. & Peters, N., SAE technical paper (liquid spray in 1-D, gas phase in 3-D) Abraham, J. & Magi, V., SAE technical paper (Virtual Liquid Source (VLS) model) Durand, P et. al, SAE technical paper (PDF approach to simulate sub-grid SAE technical paper vapor distribution) Béard et. al, SAE (CLE: Couplage Lagrangien-Eulérien) Gaseous drop Abani et. al, SAE Gas jet theory used for gas velocity

, SAE technical paper 972866 (liquid spray in 1-D, gas phase in 3-D) Abraham, J. & Magi, V.

7 VSB2 Spray Model Vsb2 stochastic Blob and Bubble model Unconditional robust Minimal number of parameters Adaptable to any CFD code feat. particle tracking *developed by Karlsson, A. (Volvo Tech. Corp.) results using OpenFOAM code are published in: Kösters, A. and Karlsson, A., SAE results using STAR-CD code are published in: Husberg, T., Denbratt, I. and Karlsson, A., SAE Eismark, J. et al., presented at Thiesel 2010, Valencia

) results using OpenFOAM code are published in: Kösters, A. and Karlsson, A.

8 Standard spray model Computational cell parcel collection of equal droplets E.g. consider the energy balance of the parcel: Problem: How can Tg be estimated if there are more than one parcel within the cell and/or there is a high evaporation rate?

9 VSB2 spray model blob parcel collection of equal droplets blob droplet size distribution (based on local instantaneous We and Oh), using break-up rate correlations by Pilch&Erdman* *Pilch, M. and Erdman, C.A., Int. J. Multiphase Flow 13(6): , 1987

Oh), using break-up rate correlations by Pilch&Erdman* *Pilch,

10 VSB2 spray model blob Normalized blob mass 1 0,5 0 accumulated droplet size distribution Normalized drop-size 1 1 blob mass mass mass mass mass 0,5 1 E.g. gas phase enthalpy source

Normalized drop-size 1 1 blob mass 2 3 10 mass

11 VSB2 spray model bubble Common spray model Gas phase in one cell used to calculate the interaction with the parcel cell VSB2 spray model Gas phase in a bubble used to calculate the interaction with the blob cell bubble parcel blob

parcel cell VSB2 spray model Gas phase in a bubble used

12 VSB2 spray model robustness relaxation equations (based on equilibrium) relaxation times momentum mass energy

13 VSB2 spray model equilibrium bubble blob Momentum: Mass & energy: 1. Mass: evaporation saturation (incl. heat of vaporization) m eq is remaining blob mass 2. Heat: T eq calculated after evaporation

14 Modifications in the dieselspray library: CERC parcel rewritten spraysubmodels atomizationmodel heattransfermodel breakupmodel injectormodel collisionmodel wallmodel dispersionmodel dragmodel evaporationmodel atomizationmodel heattransfermodel breakupmodel dragmodel evaporationmodel

injectormodel collisionmodel wallmodel dispersionmodel dragmodel

15 Numerical Set-up fuel: n-hexadecane tuned k-ε model (C 1 & σ ε ) Injector position: Default grid in all simulations: 0.5x0.5x1.0 mm cells

16 p gas = 19.5 bar Results (SAE ) Experiments: Siebers & Naber (SAE , SAE ) p gas = 168 bar p gas = 40 bar

17 Definition of liquid penetration p gas = 19.5 bar p gas = 168 bar

18 Chalmers HP/ HT spray rig* P inj = 600 bar (SAE ) CERC p gas = 30 bar T= 500 C p gas = 50 bar T = 410 C p gas = 70 bar T= 330 C p gas = 70 bar T= 500 C Vapor & liquid penetration are indistinguishable *experiments by Raúl Ochoterena, Chalmers University of Technology

19 Chalmers HP/ HT spray rig* P inj = 1200 bar (SAE ) p gas = 30 bar p T = gas = 30 bar 500 C T= 500 C p gas = 50 bar gas = 50 bar T = = 410 C 410 C CERC p gas = 70 bar T = 330 C p gas = 70 bar T = 500 C *experiments by Raúl Ochoterena, Chalmers University of Technology

20 Chalmers HP/HT spray rig, spray shape (SAE ) Exp: Shadowgraphs Sim: Temperature P inj = 1200 bar T gas = 683 K p gas = 50 bar CERC t = 0.4 ms t = 0.9 ms t = 1.4 ms t = 1.9 ms

21 Discussion Robustness + + Tuning parameters + + (sub models)

22 Discussion Time step dependence + Robustness + + Tuning parameters + + (sub models) p gas = 40 bar

23 Discussion Grid dependence Time step dependence + Robustness + + Tuning parameters + + (sub models) p gas = 40 bar p gas = 40 bar

24 Conclusions VSB2 spray model was successfully implemented in OpenFOAM VSB2 spray model combined with a tuned k-ε model predicts vapor and liquid penetration well under all tested conditions Robust! Ongoing Work Combustion (Modification of Partially Stirred Reactor (PaSR model))

25 Thank you for your attention! Anne Kösters

Computational Fluid Dynamics (CFD) and Multiphase Flow Modelling. Associate Professor Britt M. Halvorsen (Dr. Ing) Amaranath S.

Computational Fluid Dynamics (CFD) and Multiphase Flow Modelling Associate Professor Britt M. Halvorsen (Dr. Ing) Amaranath S. Kumara (PhD Student), PO. Box 203, N-3901, N Porsgrunn, Norway What is CFD?