## Download Fundamentals of Gas–Particle Flow by G. Rudinger PDF

By G. Rudinger

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2-6) and ( 3 - 1 6 ) are c o u p l e d through e q n . ( 3 - 1 7 ) . Penetration o f a particle in t h e y-direction t h e n is affected b y t h e gas veloc ity in t h e x-direction. In general, t h e e q u a t i o n s m u s t b e solved numerically, b u t an analytic s o l u t i o n can be o b t a i n e d [ 4 6 , 4 7 ] if o n e assumes t h e standard drag coefficient as represented b y e q n . ( 2 - 9 ) , so that f(Re) = 1 + (3-18) iRe ' 2 3 Division o f e q n . (2-6) b y e q n . ( 3 - 1 6 ) yields dup/dup = —{u — Up)/v v (3-19) This e q u a t i o n is generally valid and d o e s n o t d e p e n d o n t h e assumed drag coefficient; since u is c o n s t a n t , it can b e integrated and y i e l d s , for t h e pre- 27 scribed initial c o n d i t i o n s , u — Up = (u — Uj>^)v /vp P (3-20) 0 Since di; /d£ = v · d i ; / d y , ( 3 - 2 0 ) t o obtain P P P o n e c a n c o m b i n e eqns.

T h e particle approaches t h e e x p a n s i o n in equilibrium w i t h t h e gas and enters t h e e x p a n s i o n at t h e dis tance r from t h e corner. Since u = r and u = r0, conservation o f t h e radial and angular m o m e n t a can b e written as 0 0 P P d(mf)/dt = m(rO) /r + 3πϋμ(ιι — f) d(mr 6 )/dt = 3πΌμ(ν — rO)r 2 (3-43) 2 (3-44) where m = |πΖ) ρρ is t h e mass of t h e particle. After division b y m and intro d u c t i o n o f t h e relaxation t i m e r from e q n . ( 2 - 7 ) , these e q u a t i o n s t a k e t h e 3 v Particle Fig.

Particles injected across a c o n s t a n t f l o w Consider a particle t h a t is injected at s o m e angle i n t o a c o n s t a n t flow. T h e resulting m o t i o n t h e n is n o longer one-dimensional as in t h e previous e x a m ples. L e t u be t h e c o n s t a n t gas v e l o c i t y in t h e Λ:-direction and assume that in t h e x - d i r e c t i o n and t h e particle is injected w i t h a v e l o c i t y c o m p o n e n t u υ ο in the y-direction. We should like t o d e t e r m i n e t h e resulting particle trajectory and t h e particle penetration in t h e y-direction i n t o t h e f l o w .