Multicomponent Flows

Transcription

1 Mole Fracton emperature (K) ransport School of Aerospace Engneerng Equatons for Multcomponent Flows Jerry Setzman CH4 H2O HCO x 1 emperature Methane Flame Dstance (cm) ransport Eqns. -1 Copyrght by Jerry M. Setzman. All rghts resered. AE/ME 6766 Combuston School of Aerospace Engneerng Conseraton Equatons Wll examne (not dere) conseraton/transport equatons pertnent to most combuston flowfelds retan terms often dropped n studes of nonreactng flows drop some terms that usually are neglgble Include dffuse transport n conseraton equatons deeloped from Reynolds ransport heorem partal dfferental equatons Euleran framewor spatal coordnates and tme: ndependent arables ransport Eqns. -2 Copyrght by Jerry M. Setzman. All rghts resered. AE/ME 6766 Combuston 1

2 School of Aerospace Engneerng Mass Conseraton From R for dfferental control olume substantal derate t t x D Dt change flux(out) producton t tensor notaton ector notaton ransport Eqns. -3 Copyrght by Jerry M. Setzman. All rghts resered. AE/ME 6766 Combuston ransport Eqns. -4 Copyrght by Jerry M. Setzman. All rghts resered. School of Aerospace Engneerng Speces Conseraton Smlar expresson should hold for each speces n terms of speces elocty m producton t change flux(out) Source term m w W Dffuson Velocty Speces elocty V t Y w Y YV Y Y t t DY w producton Y V Dt dffuse flux change+con flux AE/ME 6766 Combuston 2

3 School of Aerospace Engneerng Veloctes otal elocty should be sum of all speces n mxture mnor speces should not contrbute much Mass aerage elocty Mass Dffuson Velocty Y V Mole aerage elocty Molar Dffuson Velocty V ransport Eqns. -5 Copyrght by Jerry M. Setzman. All rghts resered. AE/ME 6766 Combuston ransport Eqns. -6 Copyrght by Jerry M. Setzman. All rghts resered. School of Aerospace Engneerng Dffuse Fluxes From mass form of speces conseraton ncluded dffuse mass flux YV Y can wrte smlar term n mole unts dffuse molar flux J M V M From defntons of mass and molar ag. eloctes can show J sum of all dffuse fluxes leads to no net transport of total mass (or moles) n aerage reference frame AE/ME 6766 Combuston 3

4 School of Aerospace Engneerng Fluxes n (Smple) Bnary Systems If we examne the smplest case for mass dffuson 2 speces gradents n mass fracton only (not, p, etc.) Fc s Law ges us D Y but YV ransport Eqns. -7 so Copyrght by Jerry M. Setzman. All rghts resered. Y V D Y D ln Y Bnary Dffusty of speces n otherwse pure V also ln D AE/ME 6766 Combuston School of Aerospace Engneerng Fluxes n Multcomponent Systems Stll use Now need new expressons for dffuson eloctes also nclude mass dffuson by pressure and temperature gradents (but neglect body forces) ransport Eqns V W Copyrght by Jerry M. Setzman. All rghts resered. YV mx thermal dffuson coeff. (+/-) WD p p D 1 Y Y d dffuson drng force often small n comb. Mass flux of any speces depends on gradents of all other speces AE/ME 6766 Combuston 4

5 ransport Eqns. -9 School of Aerospace Engneerng Smplfed Dffuson Veloctes 1 V W mx Neglectng pressure and temperature gradents 1 V W D Wmx Can show for bnary mxture V D lny Can show for mxture domnated V DM lny by one speces (M) e.g., fuel-ar combuston (mostly N 2 ), especally lean D M nersely dependent on molec. weght of Copyrght by Jerry M. Setzman. All rghts resered. WD p p D 1 Y Y AE/ME 6766 Combuston H, H 2 hgh dffusty School of Aerospace Engneerng Momentum Conseraton stress tensor General form D P Dt 2 P p 3 scosty p x x 2 3 Y f U bul scosty body force per unt mass on speces B B x x ransport Eqns. -1 Copyrght by Jerry M. Setzman. All rghts resered. AE/ME 6766 Combuston 5