Mathematics / 4. Applied Mathematics /

O.F. Ryaboshtan, Ph.D. A.M. Milenin, Ph.D. S.M. Skofenko

Kharkov National Technical University of Agriculture after P. Vasilenko

Algorithm for calculating the surface bypass gas turbine blade

Consider the method of preparation of the equation arc flat bypass incident with points and calculated using the formula

. (1)

Its derivatives

, (2)

. (3)

Let the function has the form

, (4)

where , , - Basic linearly independent functions

, , - numerical coefficients.

Then

, (5)

. (6)

Equations (1) ... (3) with (4) ... (6) , , , , constitute a system, a relatively linear , ,

(7)

(8)

(9)

(10)

, , …, - values of the functions , , and their derivatives at ,,

, , …, - the values of the functions at the same .

Calculation algorithm:

1. choosing a set of basis functions , , ;

2. define their derivatives , , …, ;

3. find the values of functions and their derivatives at the points , ;

4. we expect the coefficients , , , , …, , , , according to (8), (9) and (10);

5. find the determinants of

(11)

6. determine the values of the coefficients

; , . (12)

7. define a function and its derivatives (4), (5), (6) with (12);

8. we find the values , , at ;

9. the results of points 7 and 8 substitute in equation (1).

In the case of an algebraic polynomial

(13)

1-9 points decision algorithm of calculation leads to an equation of bypass gas turbine blade on the site as:

(14)

The calculation is based interface surface area gas turbine blades put equation (14), but the method of calculation set out has the disadvantage that the result of the determination of derivatives at the points on the resulting equation is an accumulation of errors, resulting in the calculation process can be unstable. To avoid this, you need to solve the differential equation for determining and at the first point and assign them such that the error tended to be low. Such a process can be organized.