Design of Transonic Cascades By Conformal Transformation of the Complex Characte
Design of Transonic Cascades By Conformal Transformation of the Complex Characte
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This, in turn, leads to a further refinement of the singular solution.
Consider the system of characteristic equations (2. 17). We recall that we have, in essence, already solved (2. 17a, c), since equations (2 . 14) - (2 . 16) have the effect of specifying u and V as functions of C and n . It follows then, that we need only solve the remaining equations. Since we have already determined the form of the solution, we substitute (2. 19) into (2. 17b, d) to obtain x^ + A_y. = (X^ + \_Y^) In (?-C^)... X^+X Y-"- 2 2 2 2 ^ "^^-^ 3 3 + (x|+x_y|) In (C-?g) + -^r^ + X^ + X_Y^ = B on n= constant, and + X^ + X^Y^^ = on E, = constant.
-32- We can satisfy the first equation by setting (2. 21a) X^ + X_yJ = (2. 21b) X^ + X_Y^ = and 11 2 2 7, r, X^+X_Y^ X +X Y^ (2. 21c) X^ + X Y^ = — + ■= ^ on n = constant. Similarly, we can satisfy the second by requiring (2. 21d) X-"- + X Y"'^ = (2. 21e) X^ + X^Y^ = and n + n 2 2 r + X Y^ n + n (2. 21f) x-^ + X^Y^ = 3 3 on C = constant. Finally, if X and Y are to be regular solutions of (2.
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To quickly assess the difficulty of the text, read a short excerpt:
This, in turn, leads to a further refinement of the singular solution.
Consider the system of characteristic equations (2. 17). We recall that we have, in essence, already solved (2. 17a, c), since equations (2 . 14) - (2 . 16) have the effect of specifying u and V as functions of C and n . It follows then, that we need only solve the remaining equations. Since we have already determined the form of the solution, we substitute (2. 19) into (2. 17b, d) to obtain x^ + A_y. = (X^ + \_Y^) In (?-C^)... X^+X Y-"- 2 2 2 2 ^ "^^-^ 3 3 + (x|+x_y|) In (C-?g) + -^r^ + X^ + X_Y^ = B on n= constant, and + X^ + X^Y^^ = on E, = constant.
-32- We can satisfy the first equation by setting (2. 21a) X^ + X_yJ = (2. 21b) X^ + X_Y^ = and 11 2 2 7, r, X^+X_Y^ X +X Y^ (2. 21c) X^ + X Y^ = — + ■= ^ on n = constant. Similarly, we can satisfy the second by requiring (2. 21d) X-"- + X Y"'^ = (2. 21e) X^ + X^Y^ = and n + n 2 2 r + X Y^ n + n (2. 21f) x-^ + X^Y^ = 3 3 on C = constant. Finally, if X and Y are to be regular solutions of (2.
What to read after Design of Transonic Cascades By Conformal Transformation of the Complex Characte?
You can find similar books in the "Read Also" column, or choose other free books by Eldon a Mcintyre to read onlineMoreLess
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