Vol.3, No 15, 2003 pp. 973-980
UDC 532.546
Invited Paper
COMPRESSIBLE CHANNEL FLOW
OVER A PERMEABLE WALL
Vladan D. Djordjević
Professor, University of Belgrade, Faculty of Mechanical Engineering
27. marta 80, 11120 Belgrade, Serbia and Montenegro
E-mail: vdjordjevic@mas.bg.ac.yu
Abstract. The problem of 2-D compressible gas flow through a channel
with one permeable wall, which makes the part of the contour of a porous
body, is treated in the paper as the problem of strong interaction between
the channel flow and the flow through the porous body. Simplified equations
governing both flows are solved by using matching conditions on the permeable
wall, whereby the need for using empirically defined slip boundary conditions
by Beavers and Joseph is eliminated. Slip velocity is found to increase
down the channel attaining its maximum value, equal to the value for an
incompressible fluid, at the exit cross section of the channel. Exact expressions
for the friction coefficient and the relative increase of the mass flow
rate due to the slip are derived, and better agreement with the existing
experiments is shown to take place than by using the concept of slip boundary
conditions.
STRUJANJE STIŠLJIVOG GASA
KROZ KANAL SA POROZNIM ZIDOM
Ravansko strujanje stišljivog gasa kroz kanal sa jednim poroznim zidom,
koji čini deo konture nekog poroznog tela, tretira se u radu kao problem
jake interakcije izmedju strujanja u kanalu i strujanja kroz porozno telo.
Pojednostavljene jednačine kojima se opisuju oba strujanja rešene su korišćenjem
uslova spajanja na poroznom zidu, pri čemu se eliminiše potreba za korišćenjem
uslova klizanja fluida koji su empirijski definisali Beavers i Joseph.
Pronadjeno je da brzina klizanja raste u pravcu strujanja i da dostiže
svoju maksimalnu vrednost u izlaznom preseku kanala. Ta vrednost je jednaka
onoj koja se ima kod strujanja nestišljivog fluida. U radu su izvedene
tačne vrednosti koeficijenta trenja i relativnog povećanja masenog
protoka kroz kanal, izazvanog proklizavanjem fluida duž poroznog zida.
Dobijeni rezultati bolje se slažu sa postojećim eksperimentima, nego u
slučaju korišćenja graničnog uslova klizanja.
