Using OpenFOAM. Chen Huang PhD student CERC. Chalmers University of Technology. 5 th OpenFOAM Workshop / June 21-24, 2010, Gothenburg

Modeling of Gasoline Hollow Cone Spray Using OpenFOAM Chen Huang PhD student Department of Chalmers University of Technology

Outline 1. Motivation 2. Modifications i in OpenFOAM Library 3. Modelling of Gasoline Hollow Cone Spray 4. Conclusions

Why OpenFOAM? License free industry Motivation Promising i i features (object oriented, C++) for implementing i new models academia High demand on users Space for improvement

Modifications in OpenFOAM Library Gasoline properties http://www.tfd.chalmers.se/~hani/kurser/os_cfd_2009/chenhuang/ofproject0122.pdf 1. Properties from KIVA fuel library: 1) vapour pressure (pv), 2) heat of vapourization (hl), 3) liquid heat capacity (cp), 4) liquid enthalpy (h), 5) ideal gas heat capacity (cpg), table 6) liquid viscosity (mu), 7) liquid thermo conductivity (K), 8) surface tension (sigma), 9) molecular weight (W), 10) critical temperature (Tc).

Gasoline properties 2. Properties from thermophysical functions: 1) second virial coefficient (B) (C 8 H 18 ), 2) vapour diffusivity i i (D) (C 7 H 16 ). 3. Density (rho) is taken from the book * * Joseph A. Schetz, Allen E. Fuhs, Handbook of Fluid Dynamics and Fluid Machinery, volume one Fundamentals of Fluid Dynamics. p 156-157.

Gasoline properties 4. Properties from mixing rule * based on IC 8 H 18, C 7 H 8, and dc 7 H 16 : 1) vapour viscocity (mug), 2) vapour thermo conductivity (Kg), 3) critical pressure (Pc), 4) critical volume (Vc), 5) critical compressibility factor (Zc), 6) triple point temperature (Tt), 7) triple point pressure (Pt), 8) normal boiling temperature (Tb), 9) dipole moment (dipm), 10) Pitzer s ascentric factor (omega), 11) solubility parameter (delta). Q m y i Q i Q y m i i Q is a mixture parameter. is a liquid or vapor mole fraction. is a property of a pure liquid or vapor. i *Robert C. Reid, John M. Prausnitz, Bruce E. Poling, The Properties of Gases & Liquids Fourth Edition. p 75.

Implementation of gasoline properties Description of thermophysical functions and liquid library K_ h_ cp_ thermophysicalfunctions NSRDSfunc0 IC8H18 liquid scalar The abstract class and its sub-classes are linked with blue arrows A pink dashed arrow is used if a class is contained or used by another class. The arrow is labeled with the variable(s) () through which the pointed class or struct is accessible.

New thermophysical h functions and liquids library lb sigma_ thermophysicalfunctions NSRDSfuncgSigma gasoline liquid scalar Class gasoline based on class IC8H18 Class NSRDSfuncgSigma based on class NSRDSfunc6 Private data sigma[56]: gasoline surface tension from 0-550K with 10 K as interval. NSRDSfuncgSigma function is a linear interpolation function which returns the surface tension at specified temperature.

Check the implementation of gasoline properties Modify the break-up model which h uses the surface tension, eg, myreitzdiwakar.c Add Info commands to output the temperature e and corresponding surface tension Check the log file We got T = 320.326 sigma = 0.0163615 0163615

Modifications in OpenFOAM dieselspray Library Spray models Injector type Injector model Standard OpenFOAM Unit injector with constant Cd Hollow cone Pressure swirl Modifications in OpenFOAM Unit injector with varied Cd Pressure swirl with correct d0 Primary break-up LISA Correct LISA with correct Secondary TAB Reitz- TAB with break-up with chi-square Diwakar Collision O Rourke Trajectory Bug fixed O Rourke Bug fixed trajectory

Comparison of pdf Comparison of Rosin pdf R i R l C t R i R l n D n e D D f n D n e D n D f 1 Correct e f n = 2; = 20 m;

Test of pdf Hollow cone injector, w/o break-up model, 5000 parcels.

Comparison of CDF based on the test

Spray models Injector type Injector model Spray models Original OpenFOAM Unit injector with constant Cd Modified OpenFOAM Unit injector with varied Cd Hollow cone Pressure swirl Pressure swirl with correct d0 Secondary TAB Reitz-Diwakar TAB with break-up with chi-square Collision Bug fixed O Rourke Primary LISA Correct break-up LISA with correct Bug fixed trajectory

Comparison of droplet distribution generated by pdf Original Correct (=20 m, n=2) 03 0.3 ms asoi 06 0.6 ms asoi 10 1.0 ms asoi (T gasol =243 K, T air =350 K, p inj =200 bar)

Comparison of liquid penetration and SMD generated by pdf

Modifications to LISA atomization model D D D f D e D f D 2 2 1. Pdf after sheet break-up e D f e D f 2. SMD d 1 3 1 3 3 1 2 1 1 2 1 2 2 0 3 n n D dd f D D dd f D d SMD for distribution n=2 1 1 0 n n D dd f D d SMD 4 for distribution n=2, SMD d 3

Comparison of droplet distribution generated by LISA LISA LISA with correct 0.3 ms asoi 0.6 ms asoi 1.0 ms asoi (T gasol =243 K, T air =350 K, p inj =200 bar)

Comparison of liquid penetration and SMD generated by original and modified LISA

Comparison CDF of TAB model after droplet break-up TAB with Chi-square TAB with F x 2 3 x x 1 e x 1 x 2 6 2 3 12 12 12 1 e 1 12 2 6 F x 1 e x 2 x 0.12,12 x 0.025,4

Comparison of droplet distribution generated by TAB with Chi-square and with Chi-square 0.3 ms asoi 0.6 ms asoi 1.0 ms asoi (=40 m, n=2) (T gasol =243 K, T air =350 K, p inj =200 bar)

Comparison of liquid penetration and SMD generated by TAB with Chi-square and with

Modification of liquid sheet thickness calculated by pressure swirl injector model Pressure swirl injector is usually used with LISA atomization model. One member function d0(), returns the thickness of liquid film. According to Lisa model, ref. SAE 1999-01-0496, modification to d0 was made: 1 2 d0 d d 4A 2 d 0 d0 A d Pressure swirl injector nozzle 1 4A d d 2 2 After modification, initial droplet size is smaller; floating point error is avoided d with small injector diameter.

Comparison of droplet distribution generated by original and modified pressure swirl injector model Original Pressure swirl with correct d0 03msaSOI 0.3 06 0.6 ms asoi 10 1.0 ms asoi (T gasol =243 K, T air =350 K, p inj =200 bar)

Comparison of liquid penetration and SMD generated by pressure swirl injector model

Comparison different Cd profiles using unit injector model p 2 p inj b m Cd A v 1 2 v

Comparison of droplet distribution generated by constant and varied Cd Constant Cd Varied Cd 0.3 ms asoi 0.6 ms asoi 1.0 ms asoi Modified (=20 m,, n=2) (T gasol =243 K, T air =350 K, p inj =200 bar)

Comparison of liquid penetration and SMD generated by constant and varied Cd

Validation of gasoline spray Modified (=30 m, n=2), ReitzDiwakar (Cs=40) (T gasol =243 K, T air =350 K)

Comparison of original and modified code, Cd (T gasol =243 K, T air =350 K, p inj =200 bar)

Comparison of gasoline droplet distribution 0.18 ms asoi 0.36 ms asoi 0.64 ms asoi 0.82 ms asoi measurement original OF modified OF (T gasol =243 K, T air =350 K, p inj =200 bar)

Bugs in collision models 1. Trajectory model in mytrajectorycm.c Add a very small value when calculating the distance between two parcels. To avoid zero value in the denominator when the two parcels are in the same position. scalar dist = mag(p) + SMALL; 2. O Rourke ORourke model in samecell.h When calculating how many parcels is coalescence, the code falls into looping all the time without giving any results. // xx > collprob=zz while ((zz < xx) && (n<1000)) { zz += vnu; vnu *= nu/n; //avoid looping all the time n++; }

Comparison of collision models Hollow cone injector, modified, ReitzDiwakar (Cs=40) (T gasol =243 K, T air =350 K, p inj =200 bar)

Sensitivity of grid size (original vs modified) (=30 m, n=2), Cd, ReitzDiwakar (Cs=40), (T gasol =243 K, T air =350 K, p inj =200 bar)

Conclusions In order to accurately simulate the gasoline-ethanol l hollow cone spray, the following items were implemented/modified in OpenFOAM library: gasoline fuel property p correct distribution pressure swirl injector unit injector for varied Cd LISA bug fixed collision models Gasoline-ethanol hollow cone spray model, gives reasonably agreement with the Chalmers spray chamber experiments including droplet distribution and liquid penetration.

Thank you for your attention!