An analysis of the coupled chemically reacting boundary layer and charring ablator. Part 4 - A unified approximation for mixture transport properties for multicomponent boundary-layer applications

Sel f -cons is ten t approximations f o r b inary d i f fus ion c o e f f i c i e n t s , m u l t i component thermal d i f fus ion c o e f f i c i e n t s and mixture v i scos i ty and thermal conduct ivi ty a r e presented which g r e a t l y s implify the so lu t ion of multicomponent laminar boundary-layer problems. The bas i c premise of t h e approach is a b i fu rca t ion o f binary d i f fus ion c o e f f i c i e n t s , B . . = D/FiFj , where a reference d i f fus ion c o e f f i c i e n t and i . This expression i s exact f o r binary or te rnary systems b u t is approximate fo r l a rge r systems s ince v ( v 1)/2 Bij a r e replaced by v Fi where v i s the number of species . The Fi a r e determined by a least-squares co r re l a t ion of ac tua l d i f fus ion c o e f f i c i e n t da ta . The adequacy of t he c o r r e l a t i o n i s demonstrated fo r a number of chemical systems. D i s 13 Fi i s a d i f fus ion f a c t o r fo r spec ies The primary u t i l i t y of t he b i fu rca t ion approximation i n multicomponent boundary-layer app l i ca t ions is t h a t it enables e x p l i c i t so lu t ion of t he Stefan-Maxwell r e l a t i o n s fo r the d i f f u s i v e mass f luxes , j i . r e l a t i o n s , i n t u r n , permits the Shvab-Zeldovich t ransformation of t he spec ies conservation equat ions without introduct ion of t he concentration-dependent multicomponent d i f fus ion c o e f f i c i e n t s , D . . . I n add i t ion , an approximation t o the modified Stefan-Maxwell r e l a t i o n s provides the framework fo r t he r a t i o n a l i z a t i o n of a f i lm c o e f f i c i e n t model for d i f f u s i o n a l hea t and mass t r a n s f e r . U s e of these