Vol.1, No 7, 2000 pp. 809 - 816
UDC  621.3.035.22:514.757
SOLUTION OF THE DIRECT PROBLEM IN THEORY OF FLOW THROUGH STRAIGHT PLANE PROFILE CASCADE BY USING CONFORMAL MAPPING INTO BAND PI/2 < Im? < PI/2
Božidar Bogdanović, Saša Milanović
The Faculty of Mechanical Engineering, Niš, Beogradska 14, 18000 Niš, Yugoslavia
Abstract. In this paper, the mapping nature of flow around the profile of a straight plane cascade into band flow pi/2 < Im? < pi/2 with simetrically distributed singular points in ? = ?k, where k is a real number depending on geometric parameters of cascade, has been amalyzed. According to angles of flow at inlet and outlet of cascade as well as geometric parameters of cascade profiles, nine characteristic situations can occure, among them four belong to the group of basic mapping and five to the group of random mapping.
According to the character of variation of the velocity potential along the band contour one can conclude that the whole contour is mapped into finite part of band, so that the infinite reach of band and the decaying conformity of mapping in infinity can't make troubles in the solution of problem. The Schwartz-integrals forming the mathematical model, can be reduced to the forms with finite boundaries.
REŠAVANJE DIREKTNOG ZADATKA TEORIJE STRUJANJA KROZ PRAVE RAVANSKE REŠETKE PROFILA KONFORMNIM PRESLIKAVANJEM STRUJANJA NA POJAS PI/2 < Im? < PI/2
U radu je analiziran karakter preslikavanja strujanja oko profila prave ravanske rešetke na strujanje u pojasu pi/2 < Im? < pi/2 sa simetrično raspoređenim singularnim tačkama u ? = ?k, gde je k - realan broj, koji zavisi od geometrijskih parametara preslikavanja rešetke. Zavisno od uglova pravaca strujanja ispred i iza rešetke i geometrijskih parametara rešetke profila mogu se javiti devet karakterističnih slučajeva preslikavanja, od kojih se četiri mogu svrstati u grupu osnovnih preslikavanja, a pet u grupu slučajnih preslikavanja.
Prema karakteru promene potencijala brzine po konturi pojasa zaključuje se da se cela kontura profila praktično preslikava na ograničeni deo pojasa, pa beskrajno prostiranje pojasa i narušena konformnost preslikavanja u beskonačnosti ne stvara teškoće pri rešavanju zadatka. Schwartz-ovi integrali, koji ulaze u sistem jednačina za rešavanje zadatka, svode se na oblike sa konačnim granicama integraljenja.